Exercise problem

Question

A person is riding a bicycle, the wheels of a bicycle have an angular velocity of +17.0 rad/s. Then, the brakes are applied. In coming to rest, each wheel makes an angular displacement of +16.0 revolutions.

(a) How much time does it take for the bike to come to rest? 

_____ s 

(b) What is the angular acceleration of each wheel? 

_______ rad/s²

Answer 1

First we need to convert the angular displacement from revolutions to radians

θ = 16 rev * 2π = 32π = 100.53 rad

Now we can use

θ = ¹/₂ (ω₀ + ω_f)t

100.53 = ¹/₂ (17)t

11.83 s = t

To find α we can use

ω_f² = ω₀² + 2αθ

0 = 17² + 2α (16*2π)

-289 = 64πα

-1.437 = α