calculate the magnitude of the angular deceleration of the wheel

Question

As the brakes are applied to a bicycle wheel, the angular velocity of the wheel changes from 64 rad s^-1 to 42 rad s^-1.If the wheel turns through exactly 13 revolutions whilst the brakes are being applied

Answer 1

As the brakes are applied to a bicycle wheel, the angular velocity of the wheel changes from 64 rad s^-1 to 42 rad s^-1.If the wheel turns through exactly 13 revolutions whilst the brakes are being applied.

Find the angular acceleration

w₀= 64rad/s

wf = 42 rad/s

Number of revolution = 13 Each revolution = 2 pi

Angle = 13*2pi radian = 26 pi

use w_f² = w₀² +2 ( Angular Acceleration ) Angle covered

so 42 *42 = 64*64 + (2 α) *26 *∏

Get α from here

It will be negative means Deacceleration ( Plug in ∏ = 3.14 )