A person is riding a bicycle...

Question

A person is riding a bicycle, and its wheels have an angular velocity of 15.15 rad/s. Then, the brakes are applied and the bike is brought to a uniform stop. During braking, the angular displacement of each wheel is 13.47 revolutions. How much time does it take for the bike to come to rest?

Answer 1

Hi Faith L.,

What exactly is a uniform stop? Do you mean, a constant deceleration? (or is a patrolman stopping the bike??)

I'll assume so. Transform your stopping distance into radians. Then your standard formula for v^2 = 2ad applies. From a, you can easily obtain t: v(initial) = at

Note that radians act here just like a linear distance, and radians/sec just like a velocity.

The actual distance (not as radians equivalent!) that the bike takes to stop of course depends on the wheel diameter. But the linear acceleration is nonetheless independent of the wheel diameter.

-- Cheers, --Mr. d.