1. Circular motion T - period f =1/T - frequency -angular frequency,
or angular speed
- angular acceleration

2. Circular motion and vectorsx y

3. Comparison of Linear and Angular motion with Constant Acceleration
Fixed-axis rotation
Straight-line motion

4. Example: At t = 0, a grinding wheel has an angular velocity of 24
Example: At t = 0, a grinding wheel has an angular velocity of 24.0 rad/s. It has an constant angular acceleration of 30.0 rad/s2 until a circuit breaker trips at t = 2.00 s. From then on, it turns through 432 rad as it coasts to a stop at constant angular acceleration. What was its acceleration as it slowed down?
1) Angular speed at 2 s :
2) Angular acceleration:

5. Galilean transformations:
Relative motion
Galilean transformations:
relation between the description of a particle in two frames which are moving with respect to each other with constant velocity.
rP,B y x z B P
rP,A y x z A
rB,A

6. Clearly velocity is a reference-frame dependent quantity!
Example: Moving Sidewalk
A person walking on moving sidewalk: You can have vperson,background = 0 (not moving relative to a picture on the back wall):
Picture on the background
vp,s = -v i
bg: background
s: moving sidewalk
Vs,bg = +v i
Clearly velocity is a reference-frame dependent quantity!
VIDEO: Toy bulldozer on moving floor. (The Video Encyclopedia of Physics Demonstrations, Disk 2, Ch. 8)
What are some frame
independent quantities?
Mass, time, temperature…

7. Time for roundtrip, kid A:
Example: Two kids decide to race. Both kids walk with speed vw. One kid (A) will walk on the ground while the other (B) will walk on the “moving sidewalk” that moves with speed v0. The race is roundtrip. Which kid wins the race?
A) Kid A. B) Kid B. C) Tie. D) Depends on the ratio vw/v0. E)Depends on the sign of v0
Time for roundtrip, kid A:
Let d = length of the moving sidewalk.
Time for roundtrip, kid B:

8. Example: A boat can make it move at 5 m/s relative to the water and is trying to go across a 100-m wide river to a point on the opposite shore and right North of its starting position. The river flows due West at 3 m/s. How long does the trip take?
A. 20 s
B. 25 s
C. 33 s