1. Rotational Dynamics

2. Angle and Radian What is the circumference S ? r s
q can be defined as the arc length s along a circle divided by the radius r:
q is a pure number, but commonly is given the artificial unit, radian (“rad”) r s 
Whenever using rotational equations, you must use angles expressed in radians

3. Rigid Object A rigid object is one that is nondeformable
The relative locations of all particles making up the object remain constant
All real objects are deformable to some extent, but the rigid object model is very useful in many situations where the deformation is negligible
This simplification allows analysis of the motion of an extended object

4. Angular Displacement
The angular displacement is defined as the angle the object rotates through during some time interval
SI unit: radian (rad)
This is the angle that the reference line of length r sweeps out

5. Angular Velocity
The average angular velocity, ωavg, of a rotating rigid object is the ratio of the angular displacement to the time interval
The instantaneous velocity is defined as the limit of the average speed as the time interval approaches zero
SI unit: radian per second (rad/s)
Angular velocity positive if rotating in counterclockwise
Angular velocity will be negative if rotating in clockwise

6. Angular Acceleration
The average angular acceleration, a, of an object is defined as the ratio of the change in the angular speed to the time it takes for the object to undergo the change:

7. 𝑣 𝑜 𝑣𝑎𝑑𝑡 𝑣𝑠 𝜔 𝑜 𝜔𝛼𝜃𝑡 Raph: 𝑑= 𝑣 𝑡 Ralph: 𝜃= 𝜔 𝑡
𝑣 𝑜 𝑣𝑎𝑑𝑡 𝑣𝑠 𝜔 𝑜 𝜔𝛼𝜃𝑡
Raph: 𝑑= 𝑣 𝑡 Ralph: 𝜃= 𝜔 𝑡
Mikey: 𝑣= 𝑣 𝑜 +𝑎𝑡 Mitch: 𝜔= 𝜔 𝑜 +𝛼𝑡
Don: 𝑑= 𝑣 𝑜 𝑡+ 1 2 𝑎 𝑡 2 Dom: 𝜃= 𝜔 𝑜 𝑡+ 1 2 𝛼 𝑡 2
Leo: 𝑣 2 = 𝑣 𝑜 2 +2𝑎𝑑 Lou: 𝜔 2 = 𝜔 𝑜 2 +2𝛼𝜃
θ represents the change in the angle ( 𝜃 𝑓 − 𝜃 𝑖 ) in radians.

8. A centrifuge accelerates uniformly from rest to 15,000 rpm in 220s
A centrifuge accelerates uniformly from rest to 15,000 rpm in 220s. Through how many revolutions did it turn in this time?

9. (2.8x104 rev)

10. The tires of a car make 65 revolutions as the car reduces its speed from 95km/h to 45km/h. The tires have a diameter of 0.8m. What was the angular acceleration?

11. -4.1rad/s2