Plan for Today (AP Physics 2)
• C Testers
– Angular Motion Review – discuss and
example problems
• B Testers
– Magnetism Free Response Problems
(Individually)
Reminder
Centripetal
acceleration:
2
v
ac  ;
R
mv
Fc  mac 
R
2
Reminder - Momentum
•
More Momentum
•
Rotational Displacement, 
Consider a disk that rotates from A to B:
B

Angular displacement :
A
Measured in revolutions,
degrees, or radians.
1 rev = 360 0 = 2 rad
The best measure for rotation of
rigid bodies is the radian.
Definition of the Radian
One radian is the angle  subtended at
the center of a circle by an arc length s
equal to the radius R of the circle.
s
s

R
1 rad =
R
R
= 57.30
Angular Velocity
Angular velocity,w, is the rate of change in
angular displacement. (radians per second.)
w

t
Angular velocity in rad/s.
Angular velocity can also be given as the
frequency of revolution, f (rev/s or rpm):
w  2f Angular frequency f (rev/s).
Angular Acceleration
Angular acceleration is the rate of change in
angular velocity. (Radians per sec per sec.)
w

t
2
Angular acceleration (rad/s )
The angular acceleration can also be found
from the change in frequency, as follows:
2 (f )

t
Since
w  2 f
Angular and Linear Speed
From the definition of angular displacement:
s =  R Linear vs. angular displacement
s    R   
v


t  t   t

R

v=wR
Linear speed = angular speed x radius
Angular and Linear Acceleration:
From the velocity relationship we have:
v = wR Linear vs. angular velocity
v  v  R   v 
v

  R
t  t   t 
a = R
Linear accel. = angular accel. x radius
Angular vs. Linear Parameters
Recall the definition of linear
acceleration a from kinematics.
a
v f  v0
t
But, a = R and v = wR, so that we may write:
a
v f  v0
t
becomes
R 
Angular acceleration is the time
rate of change in angular velocity.
Rw f  Rw 0
t

w f  w0
t
A Comparison: Linear vs. Angular
 v0  v f
s  vt  
 2

t

 w0  w f
  wt  
 2
v f  vo  at
w f  wo   t
s  v0t  at
1
2
2
s  v f t  at
1
2
2
2as  v  v
2
f
2
0

t

  w 0t   t
1
2
2
  w f t  t
1
2
2
2  w  w
2
f
2
0
Problem Solving Strategy:
 Draw and label sketch of problem.
 Indicate + direction of rotation.
 List givens and state what is to be found.
Given: ____, _____, _____ (,wo,wf,,t)
Find: ____, _____
 Select equation containing one and not
the other of the unknown quantities, and
solve for the unknown.
Summary of Formulas for Rotation
 v0  v f
s  vt  
 2

t

 w0  w f
  wt  
 2
v f  vo  at
w f  wo   t
s  v0t  at
1
2
2
s  v f t  at
1
2
2
2as  v  v
2
f
2
0

t

  w 0t   t
1
2
2
  w f t  t
1
2
2
2  w  w
2
f
2
0
Moment of Inertia
• Rotational inertia
• Rotational analog to mass for linear
motion
Work on Review Materials