A bicycle that is being repaired has been turned upside down so that its wheels

Question

A bicycle that is being repaired has been turned upside down so that its wheels are free to spin. The repair technician grabs the pedal and exerts a constant torque on it, this causes the back wheel to accelerate free rest and a rate of 3.0 rad/s^2. The back wheel can be treated as a hoop with a mass of 2.5 kg and a diameter of 80 cm (a) If the back wheel goes through 12.0 complete rotations while it's being accelerated. what is its final angular velocity? (b) Rotating the pedal causes the bicycle's chain to exert a force on the sprocket attached to the back wheel; the sprocket has radius of 4.0 cm. but its moment of inertia insignificant compared to the wheel's what force did the chain apply to the sprocket to accelerate the wheel at this rate? (c) How much work did the technician do in accelerating the wheel?

Explanation / Answer

(A) wi = 0

alpha = 3 rad/s^2

theta = 12 x 2pi rad

Applying wf^2 - wi^2 = 2 alpha theta

w^2 - 0 = 2 ( 12 x 2pi) (3)

w = 21.3 rad/s

(B) torque = I alpha

= (2.5 x 0.40^2) (3) = 1.2 N m

torque = r F

1.2 = 0.04 F

F = 30 N

(C) Work done = change in KE

= I w^2 /2 - 0

= (2.5 x 0.4^2) (21.3^2) /2 = 90.74 J

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