A rider on a mountain bike is traveling to the left in the figure. Each wheel ha

Question

A rider on a mountain bike is traveling to the left in the figure. Each wheel has an angular velocity of +21.0 rad/s, where, as usual, the plus sign indicates that the wheel is rotating in the counterclockwise direction. (a) To pass another cyclist, the rider pumps harder, and the angular velocity of the wheels increases from21.0 to 27.1 rad/s in a time of 4.00 s. (b) After passing the cyclist, the rider begins to coast, and the angular velocity of the wheels decreases from +27.1 to +15.4 rad/s in a time of 9.10 s. In both instances, (a) and (b), determine the direction and magnitude of the angular acceleration (assumed constant) of the wheels.

Explanation / Answer

Here ,

for the angular acceleraiton of the wheel is a

using first equation of motion

wf = wi + a * t

27.1 = 21 + a * 4

a = 1.525 rad/s^2

the angular acceleration of the wheel is 1.525 rad/s^2 in counterclockwise direction.

b)

for the seoncd part

Using first equation of motion

wf = wi + a * t

15.4 = 27.1 + a * 9.1

a = - 1.29 rad/s^2

the angular acceleration of the wheels is 1/29 rad/s^2 in clockwise direction

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