Angular Kinematics

Equations

S = 0r

v = (omega)r

a = (alpha)r

w = change in 0 / t

alpha = change in w / t

wf = wo + alpha(t)

0 = wot + ½ (alpha) t²

wf² = wo² + 2 (alpha) 0

Torque = r F (perpendicular)

Torque = I alpha

I = mr²

Torque t = angular impulse or change in angular momentum

L (Angular momentum) = I omega

L pointmass = mvr = pr

K = ½ I omega²

mgh = ½ Iw² + ½ mv²

Total Kinetic energy in ROLLING motion = K rotational + K linear/translational

Friction causes the torque in gravitational potential energy

A disk would fall faster then a hoop because it has less inertia

counterclockwise is positive direction, clockwise is negative

when there’s multiple forces make sure to add / subtract them correctly based on if they would cause clockwise or counterclockwise rotation

remember that gravity acts on the center of an object, so a lot of the time you will use L/2

FRQ reflection

the object with less inertia will go faster

remember to cancel out mass

dont forget to use w = 2pi/t or 2pif

2 main approaches, conservation of angular momentum or torque = torque

when working with a conservation of momentum equation that has 2 objects you can write it as (i1 * i2)wf

using the momentum equation we can say that reducing radius will increase omega and decreasing mass will increase omega (increase r and m will decrease w)

if 2 objects start at rest and experience the same impulse they will have the same angular momentum

I is prerational to omega , so increasing mass will increase velocity

greater change in impulse means more kinetic energy meaning a greater omega

to find time use kinematics

Torque is inversely proportional to torque

FRICTION CAUSES TORQUE

you can look to see if theres a change in momentum to see if an object exerts torque (check to see if theres a change in omega or inertia)

a bug walking on a spinning disk that is not in the system will decrease its momentum

FORCES ALWAYS ACT IN THE MIDDLE AT L/2 or R/2