# Chapter 11-12 Key Equations and Ideas ```AP Physics Chapter 11-12 Key Equations and Ideas
Kinematic Equations
Rotation
(constant ang accel)
s = r
d
dt
d
 
dt
v = r

a = r
KR = &frac12;I2
f = i + it + &frac12;t2
f2 = i2 + 2(f – i)
f = i + t
f = i + &frac12;(f + i)t
n
ac = 2r
I 
m r
i 1
dm = dV
2
i i
2
dV = 4r dr (spherical)
(discrete)
I
r
2
dm (distributed)
I = Icom + Mh2 (parallel axis theorem)
Torque
Rotational Work and K
 = r x F = rF sin = rF  rF = I
W = K = &frac12;If2 - &frac12;Ii2
Angular Momentum


dL

L = I net 
L  r̂ x p̂
dt
dL
When net = 0,
0
dt
 Lf = Li (always)
 Iff = Iii
W=

f
i
 d
W = (f - i) (constant )
d ( )
dW

 
dt
dt
g
Yo-Yo: acom 
I
1  com2
MR
P 
 CW = CCW
Key Ideas:

An angular displacement in the counterclockwise direction is positive and one in the
clockwise direction is negative.

To find the extreme value (e.g. minimum or maximum) of a function, take the derivative
and set it equal to zero.

All the linear quantities and equations have corresponding angular quantities and equations.
Remember the linear equations and you can immediately write the angular equations by
substituting in the corresponding angular quantities.

Always remember to use radians, not degrees in the equations above.

In rotational motion, there can be tangential acceleration (i.e. in the direction of the
velocity vector) and radial acceleration (i.e. pointing towards the center of rotation).

A body will freely rotate about an axis that always passes through the center of mass of
the body. If a body is forced to rotate about an axis that does not pass through the
center of mass, use the Parallel Axis Theorem to calculate its rotational inertia.

A body with translational motion has linear kinetic energy. A body that only rotates has
rotational kinetic energy. A rolling body has both linear and rotational kinetic energy.

The sum of all the torques acting on a particle or on a system of particles is equal to the
time rate of change of the angular momentum of that particle or the system or particles,
respectively.

If the net external torque acting a system is zero, the angular momentum of the system
remains constant, no matter what changes take place within the system.

If the component of the next external torque on a system along a certain axis is zero,
then the component of the angular momentum of the system along that axis cannot change,
no matter what changes take place within the system.

Conservation of angular momentum always holds in a closed (i.e. no matter passes in or out)
and isolated (i.e. no external forces) system. Angular momentum is conserved in each
dimension!!
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