AP Physics Study Guide Chapter 8 & 9
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AP Physics Study Guide Chapter 8 & 9: Rotational Velocity Angular quantities = ! ! = 2 Degrees to radians: 32.58 = !!"#$ !"# One radian = 57.3 Angular velocity = ∆! ∆! !"#$%"$%"&’(# = !" !" Angular acceleration Counterclockwise is positive ∝= ∆! ∆! Rotational to translational ∆ = ! + ! ! ! ! ! = ! ! + 2 ∝ ∆ ∆ = ! ! ! − ! ! = tan = ∝ !"!#$ = ∝ ! + ! ! ! ! ! ! = ! Dynamics rotational motion Cause of rotation is torque = sin = ∝ Is the moment of inertia mass distribution about a rotating point = ! = 0 Energy ∆ = 0 ℎ ! = ! ! ! ! + ! ! ! = ! ! ! ! = Rolling motion = ∆! ∆! = ∆! ∆! ∆ = ! ! − ! ! Assume there is no slipping “burn out” means we have static friction Wheel rolling is a combination of rotational and translational motion Revolutions is linear distance/circumference Angular dynamics
Transcript of AP Physics Study Guide Chapter 8 & 9
AP Physics Study Guide Chapter 8 & 9: Rotational Velocity v Angular quantities
Ø 𝜃𝑟𝑎𝑑 = !!
Ø 𝑙 = 2𝜋𝑟 Ø Degrees to radians: 32.58 = !!"#$
!"#
Ø One radian = 57.3 Ø Angular velocity
§ 𝜔 = ∆!∆!
§ 𝜔!"#$%"$%"&'(# =!"!"
Ø Angular acceleration § Counterclockwise is positive § ∝= ∆!
∆!
Ø Rotational to translational § ∆𝜃 = 𝜔!𝑡 +
!!𝑎𝑡!
§ 𝜔!! = 𝜔!! + 2 ∝ ∆𝜃 § ∆𝜃 = !
!𝜔! − 𝜔!
§ 𝑣! = 𝜔𝑟 § 𝑎 tan = 𝑟 ∝
§ 𝑎!"!#$ = ∝ 𝑟 ! + !!!
!
!
§ 𝜔!𝑟 = 𝑎! v Dynamics rotational motion
Ø Cause of rotation is torque Ø 𝜏 = 𝐹𝑑 sin𝜃 Ø 𝜏 = 𝐼 ∝
§ 𝐼 Is the moment of inertia mass distribution about a rotating point Ø 𝐼 = 𝑚𝑟! Ø 𝜏 = 0
v Energy Ø ∆𝐸 = 0 Ø 𝑚𝑔ℎ! =
!!𝑚𝑣!! +
!!𝐼𝜔!
Ø 𝐾𝐸 = !!𝐼𝜔!
Ø 𝑣! = 𝜔𝑟 v Rolling motion
Ø 𝜏 = ∆!∆!
Ø 𝐹 = ∆!∆!
Ø ∆𝐿 = 𝐼!𝜔! − 𝐼!𝜔! Ø Assume there is no slipping “burn out” means we have static friction Ø Wheel rolling is a combination of rotational and translational motion Ø Revolutions is linear distance/circumference
v Angular dynamics
Ø 𝜏 = 𝐼 ∝ § 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑠 𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝜔
Ø 𝐼 = 𝑚𝑟! § 𝑐𝑦𝑙𝑖𝑛𝑑𝑒𝑟: 𝐼 = !
!𝑚𝑟!
§ 𝑟𝑜𝑑 𝑎𝑏𝑜𝑢𝑡 𝑠𝑜𝑚𝑒 𝑒𝑛𝑑: 𝐼 = !!𝑚𝐿!
§ 𝑠𝑜𝑙𝑖𝑑 𝑠𝑝ℎ𝑒𝑟𝑒: 𝐼 = !!𝑚𝑟!
§ ℎ𝑜𝑜𝑝 𝑜𝑟 𝑝𝑜𝑖𝑛𝑡 𝑝𝑎𝑟𝑡𝑖𝑐𝑙𝑒: 𝐼 = 𝑚𝑟! § Assume density is uniform
Ø 𝐹 = 𝑚𝑎,𝑎 =∝ 𝐹 = 𝑚𝑟 ∝ 𝐹 𝑥 = 𝑚𝑟! ∝ 𝜏 = 𝐹𝑟
v Torque Ø Cause of rotation or motion Ø 𝜏 = 𝐹𝑟 sin𝜃 Ø 𝜏 = 𝐹!𝑟
v Kinetic energy with this stuff Ø 𝐾𝐸!"#$#%"&$' =
!!𝐼𝜔!
Ø 𝑣 = !!!!!!
v Angular momentum
Ø Linear = 𝑝 = 𝑚𝑣 Ø Angular = 𝐿 = 𝐼𝜔 Ø 𝜏∆𝑡 = 𝐼𝜔! − 𝐼𝜔!
