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?
(a) How much time does it take for the bike to come to rest?
(b) What is the angular acceleration of each wheel?
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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
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