HELP!! 10 points!! A person is riding a bicycle, the wheels of a bicycle have an angular velocity of...
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# HELP!! 10 points!! A person is riding a bicycle, the wheels of a bicycle have an angular velocity of...

[From: ] [author: ] [Date: 11-05-20] [Hit: ]
t = ωo / α = 24/2.865 = 8.......
A person is riding a bicycle, the wheels of a bicycle have an angular velocity of +24.0 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?

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

-
First find the deceleration of the wheel by employing the
following well-known kinematic equation equating initial
and final angular velocity with angular displacement.

ω² = ωo² - 2αθ

where,
initial angular velocity: ωo = 24 rad/s
final angular velocity: ω = 0
angular displacement: θ = 16*2π = 32π rad
angular deceleration: α

α = 24²/64π = 2.865 rad/s²

Now that we have the angular deceleration, we can employ
another well-known kinematic equation:

ω = ωo - αt

Solving for t:

t = ωo / α = 24/2.865 = 8.377 s
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