Question

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

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

Answer 1

The bicycle's velocity is 12m/s, and its angular velocity is 0.75 rad/s, using centripetal acceleration and radius formulas for circular motion.

Step-by-step explanation:

The velocity (v) of a bicycle moving in a circle with a radius (r) of 16m and a centripetal acceleration (ac) of 9m/s² can be found using the formula:

ac = v² / r

By rearranging this equation we get:

v = √(ac × r)

Substitute ac = 9m/s² and r = 16m:

v = √(9m/s² × 16m) = √144m²/s² = 12m/s

The angular velocity (ω) can be calculated by the formula:

ω = v / r

ω = 12m/s / 16m = 0.75 rad/s

Therefore, the correct answer is:

v = 12m/s, ω = 0.75 rad/s