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Transcript of Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory...
![Page 1: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/1.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 2: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/2.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 3: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/3.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 4: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/4.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation
+Review of Introductory Rotational Dynamics+Combined translation and rotation
+Rolling without slipping+Rolling with slipping
+Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia
![Page 5: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/5.jpg)
Examples of rotation: Earth
To find the direction of omega, apply the right hand rule as follows:
With fingers curling in direction of rotation, the thumb gives direction of omega
i.e. direction of earth’s omega is upward
![Page 6: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/6.jpg)
rotation of the sky
star trails
centered on Polaris
rotate once a day
![Page 7: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/7.jpg)
rotation can be fun
![Page 8: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/8.jpg)
sometimes the goal is rotational equilibrium
• 1st condition for equilibrium:
Fnet = 0
• 2nd condition for equilbrium:
torque net = 0
• i.e., torque ccw = torque cw
![Page 9: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/9.jpg)
rotational equilibrium again
![Page 10: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/10.jpg)
sometimes the goal is large rotational velocity
![Page 11: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/11.jpg)
M31 rotates once every few hundred million years
![Page 12: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/12.jpg)
Katrina rotated
![Page 13: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/13.jpg)
a generic kidney shaped object rotates about a fixed axis:
a thing of beauty is a joy forever!
![Page 14: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/14.jpg)
a turbine (driven by moving fluid) rotates about a fixed axis
![Page 15: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/15.jpg)
a jet engine rotates about a fixed axis
![Page 16: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/16.jpg)
![Page 17: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/17.jpg)
steam driven power plant turbine:imagine this thing rotating at 60 hz
generating your electricity
![Page 18: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/18.jpg)
electric motors are backwards connected generators:
they are still mechanical rotators about a fixed axis
![Page 19: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/19.jpg)
electric motors power our elderly friends’ scooters
![Page 20: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/20.jpg)
and nuclear subs also(when they are submerged)
![Page 21: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/21.jpg)
gears rotate about a fixed axis
![Page 22: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/22.jpg)
gear attached to an electric motor(sounds like a good idea to me)
![Page 23: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/23.jpg)
nanotechology electric motor gear (the gear teeth are smaller than a red blood cell)
rotating about a fixed axis, imaged with an electron microscope
(end of examples of rotation)
![Page 24: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/24.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 25: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/25.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Examples of Rotation
+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 26: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/26.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Examples of Rotation
+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 27: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/27.jpg)
Rotational Kinematics
• Θ = angular position wrt arbitrary origin
• Δθ = angular displacement (rad)
• ω = Δθ / Δt = dθ / dt (rad/s)
• α = Δ ω / Δt = d ω / dt = d2θ / dt2 (rad/s2)
• s = r θ• v = r ω• a = r α
![Page 28: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/28.jpg)
α = constant implies
• Δθ = ω0t + ½ αt2
• ω = ω0 + α t
• ω2 = ω02 + 2 α Δθ
• Δθ = ½ (ω0 + ω) t
• If α is variable, you need calculus
![Page 29: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/29.jpg)
Intro Rotational Dynamics
• Г = τ = r x F
• I = Σ mi ri2 (collection of point masses)
= ∫ r2 dm (continuous matter distribution)
• I total = I 1 + I 2 + I 3 + … (composite object)
• Fnet = ma becomes Гnet = τnet = I α
![Page 30: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/30.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 31: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/31.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 32: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/32.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation
+Rolling without slipping+Rolling with slipping
+Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia
![Page 33: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/33.jpg)
Earth revolves (translation of cm) and rotates about cm
![Page 34: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/34.jpg)
Look Ma, no hands
![Page 35: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/35.jpg)
combined translation and rotation
Ktotal = Ktranslational + Krotational
= Kof the cm + Karound the cm
= ½ mv2 + ½ I ω2
![Page 36: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/36.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 37: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/37.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation
+Rolling without slipping+Rolling with slipping
+Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia
![Page 38: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/38.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation
+Rolling without slipping+Rolling with slipping
+Rotational form of Conservation Laws +Collisions involving objects having Moment of Inertia
![Page 39: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/39.jpg)
linear and angular velocity and acceleration are proportional
![Page 40: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/40.jpg)
rolling without slipping in our golden years
![Page 41: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/41.jpg)
rolling without slipping
• v = ω r (use with energy conservation)
• atangential = α r (use with 2nd laws)
• friction acts, but does no work
• energy conserved as Wnc = 0
![Page 42: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/42.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping (pure rolling)
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 43: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/43.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping (pure rolling)
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 44: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/44.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping (pure rolling)
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 45: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/45.jpg)
linear and angular velocities and accelerations are independent,
i.e., he’s not getting very much bang (v) for his buck (ω)
![Page 46: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/46.jpg)
don’t try this at home
![Page 47: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/47.jpg)
rolling with slipping
• v ≠ ω r• atangential ≠ α r
• apply Fnet = ma to find atangential of the cm• apply Гnet = Iα to find α around the cm
• to compute t where pure rolling sets in, set a(t) = α(t) r, where a(t) and α(t) are solutions of force and torque equations
![Page 48: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/48.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 49: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/49.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping
+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 50: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/50.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping
+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 51: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/51.jpg)
definition of angular momentum:
• L = r x p = r x mv (point m moving at v)
• L = I ω (rigid body with moment I)
![Page 52: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/52.jpg)
law of motion in terms of L:
torque net = ΔL/ Δt = dL / dt
![Page 53: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/53.jpg)
Conservation of angular momentum:
if torque net = 0, then dL / dt = 0
and so, L = constant
so, I initial ω initial = I final ω final (ice skater)
![Page 54: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/54.jpg)
easier said than done
![Page 55: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/55.jpg)
The agony of defeat(net torque ≠ 0, L not conserved)
![Page 56: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/56.jpg)
The thrill of victory(net torque = 0, L conserved)
![Page 57: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/57.jpg)
Conservation of energy, including rotation
Simply allow for rotational
as well as translational K
![Page 58: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/58.jpg)
Conservation of linear momentum
…is not affected by rotational motion, but applies to the cm of the body as before
(i.e., if Fnet,ext = 0 on system. That is,
if something is nailed down and rotates, linear momentum is not conserved, but L can be)
![Page 59: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/59.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 60: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/60.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of Inertia
![Page 61: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/61.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions involving objects having Moment of
Inertia
![Page 62: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/62.jpg)
Advanced Rotational Dynamicsfor AP Physics
+Common Examples of Rotation+Review of Introductory Rotational Dynamics
+Combined translation and rotation+Rolling without slipping
+Rolling with slipping+Rotational form of Conservation Laws
+Collisions (and other systems)
involving objects having Moment of
Inertia
![Page 63: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/63.jpg)
…this is rather important on the AP Exam…
![Page 64: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/64.jpg)
Unfortunately, few common practical applications exist for this type of problem.
They are simply artificially contrived
![Page 65: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/65.jpg)
Any or all 3 conservation laws of energy, linear momentum, and angular
momentum may be satisfied!You have to figure out which ones are
operating, if they don’t tell you!
• If Wnc = 0, then Einitial = Efinal
• If Fnet,ext = 0, then pinitial = pfinal
• If Гnet = 0, then Linitial = Lfinal
![Page 66: Advanced Rotational Dynamics for AP Physics +Common Examples of Rotation +Review of Introductory Rotational Dynamics +Combined translation and rotation.](https://reader035.fdocuments.net/reader035/viewer/2022081519/56649da05503460f94a8ba5b/html5/thumbnails/66.jpg)
The End
That’s it! Now go make a 5!