A bicycle is being ridden down a street and is accelerating. The bicycle wheels,

Question

A bicycle is being ridden down a street and is accelerating. The bicycle wheels, starting from rest, had a torque placed on them that caused the wheels to have a constant angular acceleration of .7rad/s2. There is a broken spoke on one of the wheels. (it is broken so that you can keep track of it.) The broken spoke initially makes an angle of 25 deg with respect to the road (horizontal).

a) How many revolutions does the wheel make in the first 15 seconds after the torque is applied?

b) What angle does the spoke make with respect to the horizontal (the positive x-axis) at the end of the 15 second period?

c) What is the final angular velocity of the wheel?

d) If the wheel has a radius of .5m and there is a piece of gum stuck to the edge of the wheel, what is the speed of the gum at the end of this 15 second period?

Explanation / Answer

given,

acceleration = 0.7 rad/sec^2

initial velocity = 0 m/s

time = 15 sec

s = ut + 0.5 * at^2

s = 0 + 0.5 * 0.7 * 15^2

s = 78.75 rad or 4512.0426 degree

revolution = 4512.0426 / 360

revolutions does the wheel make in the first 15 seconds = 12.533

angle spoke will make = 0.533 * 360

angle spoke will make after 15 sec = 192.04 degree

v = u + at

v = 0 + 0.7 * 15

final velocity = 10.5 rad/sec

linear speed = angular speed * radius

speed of the gum = 10.5 * 0.5

speed of the gum = 5.25 m/s

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