AP Physics 1 ~ Torque & Rotational Motion Test Review

angular and linear (translational) velocity relationship

v=ωr

angular velocity

ω=⯅θ/⯅t

linear velocity (translational)

v=⯅d/⯅t

angular displacement

θ

linear displacement (translational)

s

parallel axis theorem

describes how to find the moment of inertia (𝐼) of a rigid body about any axis, given its moment of inertia about a parallel axis through its center of mass (𝐼_cm), by adding the product of the body's total mass (m) and the square of the perpendicular distance (d) between the two axes:

𝐼=𝐼_cm+md²

torque

𝜏=rFsinθ

𝜏=𝐼𝛼

𝜏=P/ω

work done by torque

W=𝜏⯅θ

angular momentum

L=𝐼ω

linear momentum (translational)

p=mv

moment of inertia

measures an object's resistance to changes in its rotational motion

𝐼=∑mr²

angular acceleration

α=⯅ω/⯅t

linear acceleration (translational)

a=⯅v/⯅t

angular and linear (translational) acceleration relationship

a=rα

angular and linear (translational) displacement relationship

s=rθ

rotational kinematics

use linear kinematics equations and replace values with the corresponding angular values

angular velocity (using frequency)

ω=2πf

angular velocity of a rotating object is equal to 2π times its frequency of rotation

change in angular momentum (angular impulse)

⯅L=𝜏⯅t

example (hollow sphere): ⯅L=(2/3)RMg⯅t

angular momentum of object moving in a straight line

L=rmvsinθ

unit circle

circle with a radius of 1 (circumference 2π)

centripetal acceleration (UCM)

a_c=rω²

rotational kinetic energy

use rotational equivalent velocity and substitute into the kinetic equation:

KE_R=(1/2)m_ir_i²ω² = (1/2)Iω²