An exhausted bicyclist pedals somewhat erratically, so that the angular velocity of his tires follows the equation

w(t)=(1/2)t-(1/4)sin (2t) for t>= 0,

where t represents time (measured in seconds).

1) Express the angular displacement undergone by the spot of paint at t=2 seconds in degrees.

2) What distance, d, has the spot of paint moved in 2 seconds if the radius of the tire is 50 centimeters?

3) Which one of the following statements describes the motion of the spot of paint at t=2.0 seconds?

a)The angular acceleration of the spot of paint is constant and the magnitude of the angular speed is decreasing.

b) constant and speed is increasing

c) positive and speed is decreasing

d) positive and speed is increasing

e) negative and speed is decreasing

f) negative and speed is increasing

– I have solved a prob. with this asking for angular displacement between 0 and 2 seconds when t=0 and theta=0(angle). which I got theta = .793 rad which is correct

### 1 Answer

For the first problem just convert .793 rad into degrees

For the second problem d = radius*theta(in rad)

For the third problem d) positive and speed increasing: use the angular acceleration formula(derivative of angular velocity) and see that it comes out positive