When an object spins, It is said to undergo Rotational motion.
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Transcript of When an object spins, It is said to undergo Rotational motion.
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When an object spins, It is said to undergo Rotational motion.
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When measuring rotational Motion, we will use radians.
A radian is an angle whose Arc length is equal to its radius,
Which is approximately Equal to 57.3°
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θ = sr
θ = the angle
r = the radius
s = arc length
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360° = 2π rad
We now have a conversionBetween radians and degrees.
θ (rad) = π180°
θ (deg)
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Ben, riding on a carousel, Travels through an arc length of
11.5 m. If the carousel has a Radius of 8 m, what is the angular
Displacement? What degree is this?
2.88 rad 165°
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Angular speed describes The rate at which a body
Rotates about an axis, usuallyExpressed in rad/s.
ω = ΔθΔt
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Ben now spins on a stool, if heTurns clockwise through 10π rad,
During a 10 s interval, what isThe average angular speed
Of his feet?
3.14 rad/s
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Angular acceleration is the timeRate of change of angular speed,
Usually expressed in radians Per second per second.
α = ΔωΔt
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Now Ben rotates on the stoolWith an initial angular speed of
21.5 rad/s. The stool accelerates,And after 3.5s, the speed is 28
rad/s. What is the average Angular acceleration?
1.9 rad/s/s
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Rotational
Motion
Linear
Motion
ωf = ωi + αΔt vf = vi + aΔt
Δθ = ωiΔt + ½α(Δt)2 Δx = viΔt + ½a(Δt)2
ωf2 = ωi
2 + 2α(Δθ) vf2 = vi
2 + 2aΔx
Angular Kinematics
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The wheel on an upside-down bikeRotates with a constant angular Acceleration of 3.5 rad/s/s. If the Initial angular speed of the wheelIs 2 rad/s, through what angular
Displacement does the wheelRotate in 2 sec?
11 rad
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Torque is a quantity that measuresThe ability of a force to rotate
An object around some axis
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Torque is a scalar quantity.
Torque has the SI unit of N*m
τ = Fd(sinθ)
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Torque is positive or negative Depending on the directionThe force tends to rotate
An object.
Torque that is clockwise isDefined as negative.
Thus torques that produce a Counterclockwise rotation are
Defined to be positive.
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Find the torque produced by a 3 N force applied at an angleOf 60° to a door 0.25m from
The hinge.
0.65 N m
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In order to calculate the moment Of inertia, you have to use theFormulas provided in the bookFor the many different shapes.
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Shape Formula for moment of inertia
Thin hoop about symmetry of object
MR2
Thin hoop about diameter 1/2 MR2
Point of mass about axis MR2
Disk about axis 1/2 MR2
Rod about axis through center 1/12 ML2
Rod about axis through end 1/3 ML2
Solid sphere about diameter 2/5 MR2
Thin sphere shell about diameter
2/3 MR2
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A 5m horizontal beam weighing 315N is attached to a wall so That it rotates. Its far end is
Supported by a cable at an angleOf 53°, and a 545N is standing
1.5m from the wall. Find the tensionAnd the force on the beam by the
Wall, R.
Tension = 403 N R = 590N
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Newton’s 2nd Law for Rotating objects.
τ = Iα
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A catapult propels a 0.150 kgStone. The length of the
Catapult arm is 0.350m. If the Stone leaves the catapult with an
Acceleration of 100 m/s2, whatIs the torque exerted on the stone.
5.25 Nm
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The center of mass of an objectIs the point at which all the
Mass of the body can be Considered to be concentrated
When analyzing Translational motion.
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Rotational and translationalMotion can be combined.
The moment of inertia is theRotational analog of mass.
Equilibrium requires zero net force,And zero net torque.
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A 5.8 kg ladder, 1.8 m long, restsOn 2 saw horses. Sawhorse A is 0.6 m from one end of the ladder
And sawhorse B is 0.15 m from theOther end of the ladder. What force
Does each sawhorse exert on the Ladder?
Fb = 16 N Fa = 41 N
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The centrifugal force is anApparent force.
NOT A REAL FORCE!
It is not a real force because thereIs no physical outward push.
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The Coriolis Force is also a FAKE FORCE!
This is because it is only apparentTo rotating observer.
This is very apparent on Earth However. It is the reason forThe direction of the winds.
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