4. The wheel of your bike is spinning at a constant angular velocity of 15rad/s

Question

4. The wheel of your bike is spinning at a constant angular velocity of 15rad/s when you apply the brakes bringing your bike to a stop in 7s. Assume you apply even pressure and cause a constant torque on the wheel with the brake pads. Find (a) (2 points) the constant angular acceleration of the wheel, b) (2 points) the total angular displacement of the wheel in coming to a stop (c) (2 points) If the wheel can be modeled as a thin ring with a diameter of 62cm and a mass of 2.8kg, find the torque caused by the brake pads.

Explanation / Answer

(A) wf = wi + alpha t

0 = 15 + 7 alpha

alpha = - 2.14 rad/s^2

(minus sign tells that angular acceleration is in opposite direction of velocity.)

(B) wf^2 - wi^2 = 2 alpha theta

0^2 - 15^2 = 2(-2.14)(theta)

theta = 52.5 rad

(C) torque = I alpha  

and I = M R^2 = (2.8 kg) (0.62 m / 2)^2

I = 0.269 kg m^2

torque = (0.269) (2.14) =0.577 N m

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