A bicycle wheel of radius 0.50 m is rolling without slipping on a horizontal sur

Question

A bicycle wheel of radius 0.50 m is rolling without slipping on a horizontal surface with an angular speed of 3pie rad/s when the cyclist begins to uniformly apply the breaks. The bicycle stops in 4.0 s.

1. what is the angular deceleartion in radians second squared of the bicycle wheel?
2. What is the linear deceleration of the bicycle in m/s2
3. What is the initial tangential velocity of the bicycle wheel?
4. What angular displacement did the bicycle wheel rotate during the 4.0 seconds of braking?
5. How far did the bicycle travel during the 4.0 seconds of breaking?

Explanation / Answer

1.i = 3 rad/s ; t_stop= 4s

=(f - i )/t ;here f =0;t= t_stop= 4s

= -2.355 rad/s2

2. a=R = -2.355 rad/s2 * 0.50m = 1.1775 m/s2

3.tangential velocity = i * R =1.5 m/s

4.angular displacement=(f2 - i2) /2 = 18.84 rad

5.distance travelled by bicycle = angular displacement*R = 9.42m

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