Alice and Bob are each riding horses on a carousel. Alice's horse is twice as far from the axis of spin of the carousel as Bob's horse. Let ω A be the angular velocity of Alice's horse, and let ω B be the angular velocity of Bob's horse. Which of the following is true?

a. ω A = ω B

b. ω A > ω B

c. ω A < ω B

option (a)

Explanation:

the angular velocity of the carousel is same througout the motion, so the angular velocity of all the horses is same, but the linear velocity is different for different horses.

As the angular displacement of all the horses are same in the same time so the angular velocity is same.

The relation between the linear velocity and the angular velocity is given by

v = r ω

where, v is linear velocity and r be the distance between the horse and axis of rotation and ω be the angular velocity.

So, the angular velocity of Alice horse is same as the angular velocity of Bob horse.

ωA = ωB

Thus, option (a) is true.