An Exhausted Bicyclist

Learning Goal:

To understand rigid-body rotation about a translating axis.

An exhausted bicyclist pedals somewhat erratically. The angular velocity of the front tire, as measured with respect to an axis fixed at the tire’s center, is given by

ω(t)=12t−14sin(2t)fort≥0

where t represents the time in seconds and ω(t) is measured in radians per second. Assume that the tires roll without slipping.

Part A

The bicycle’s front tire has a spot of paint on it. Take the spot’s position at time t=0.00s to be at angle θ=0.00radians with respect to an axis parallel to the ground (and perpendicular to the axis fixed at the tire’s center) and take angles in the direction of the tire's rotation to be positive. What angular displacement θ(2) has the spot undergone between 0.00 and 2.0 s?

 

theta (2) =

0.793

radians

 

Part B

If the tire’s radius is 23 cm, what is d, the magnitude of the spot’s displacement after 2.0 seconds?

Express your answer numerically to two significant figures in centimeters.

d =

18

cm

Part C Which one of the following statements describes the spot’s motion at t=2.0s?   positive and the angular velocity’s magnitude is increasing.