Question

A bicycle is moving on a cycling track of radius 16m. The centripetal acceleration is 9m/s². Find the velocity and angular velocity:

a) v = 25 m/s, w = 25/16 rad/s
b) v = 50 m/s, w = 3.125 rad/s
c) v = 12 m/s, w = 0.75 rad/s
d) v = 16 m/s

Answer 1

To find the velocity and angular velocity of a bicycle on a cycling track, we use the centripetal acceleration and the track's radius. The correct answer is c) v = 12 m/s, w = 0.75 rad/s.

Step-by-step explanation:

To find the velocity and angular velocity of a bicycle moving on a cycling track, we can use the centripetal acceleration and the radius of the track.

The formula for centripetal acceleration is a = v^2 / r, where v is the velocity and r is the radius.

Given that the centripetal acceleration is 9 m/s² and the radius is 16 m, we can rearrange the formula to find the velocity:

v = sqrt(a * r) = sqrt(9 * 16) = 12 m/s

Since the angular velocity is related to the linear velocity by the formula v = w * r, we can rearrange the formula to find the angular velocity:

w = v / r = 12 / 16 = 0.75 rad/s

Therefore, the correct answer is c) v = 12 m/s, w = 0.75 rad/s.