2. Rotational Kinematics with Constant Angular Acceleration

3. Rotational Kinematics with Constant Angular Acceleration

4. A ceiling fan, set on low, is turning at 95. 0 rpm
A ceiling fan, set on low, is turning at 95.0 rpm. After it is switched to medium, it takes 3.75 s to get up to 155 rpm. Assuming constant angular acceleration, find a.

5. A ceiling fan always changes speed at the same angular acceleration, 1
A ceiling fan always changes speed at the same angular acceleration, 1.68 s-2. When it is turned on (from rest), it reaches its high setting, 195 rpm, in t seconds. Through what angular displacement does it turn in those t seconds?

6. Connections between Linear and Rotational Quantities

7. Connections between Linear and Rotational Quantities
There is a connection between the angular velocity of something in circular motion, and its tangential velocity:

8. Connections between Linear and Rotational Quantities
There is a connection between the angular velocity of something in circular motion, and its tangential velocity:

9. Connections between Linear and Rotational Quantities
There is a connection between the angular velocity of something in circular motion, and its tangential velocity:

10. Connections between Linear and Rotational Quantities
There is a connection between the angular velocity of something in circular motion, and its tangential velocity:

11. Connections between Linear and Rotational Quantities
There is a connection between the angular velocity of something in circular motion, and its tangential velocity:

12. one-quarter of Bonnie’s. four times Bonnie’s.
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one complete revolution every 2 seconds. Klyde’s angular velocity is
the same as Bonnie’s.
twice Bonnie’s.
half of Bonnie’s.
one-quarter of Bonnie’s.
four times Bonnie’s. ω
Bonnie
Klyde
Answer: A

13. They both have the same linear velocity.
Bonnie sits on the outer rim of a merry-go-round, and Klyde sits midway between the center and the rim. The merry-go-round makes one revolution every 2 seconds. Who has the larger linear (tangential) velocity?
Klyde
Bonnie
They both have the same linear velocity.
Linear velocity is zero for both of them. ω
Bonnie
Klyde
Answer: B

14. A child sits 1. 45 m from the center of a playground merry-go-round
A child sits 1.45 m from the center of a playground merry-go-round. If the merry-go-round turns with a period of 1.75 s, what is the child’s tangential velocity?

15. A child sits 1. 45 m from the center of a playground merry-go-round
A child sits 1.45 m from the center of a playground merry-go-round. If the merry-go-round turns with a period of 1.75 s, what is the child’s tangential velocity?
What is the child’s centripetal acceleration?

16. Centripetal acceleration:

17. Centripetal acceleration:
What about tangential acceleration at?

18. Centripetal acceleration:
What about tangential acceleration at?

19. So now we have a full set of equations relating linear and rotational quantities:

20. So now we have a full set of equations relating linear and rotational quantities:

21. So now we have a full set of equations relating linear and rotational quantities:

22. A carnival carousel starts from rest and speeds up with constant angular acceleration to its full operating speed. While it is speeding up, does the total acceleration experienced by a rider…
A) Increase
B) Decrease
C) Remain constant

23. A carnival merry-go-round starts from rest, reaching its operating speed in 12.0 s, at which time it turns with a period of 5.50 s. What is the magnitude of the total acceleration of a horse that is 3.25 m from the center, 6.00 s after starting from rest, assuming constant angular acceleration?