Angular Velocity with Bike Tires

[Spartan301]

Homework Statement

Your bicycle tires have a radius of 0.33 m. It takes you 850 seconds to ride 14 times counterclockwise around a circular track of radius 73 m at a constant speed. (a) What is the angular velocity of the bicycle around the track? (b) What is the magnitude of the angular velocity of a tire around its axis? (That is, don’t worry about whether the tire’s rotation is clockwise or counterclockwise.)

Tire Radius = 0.33 m
Time : 850
14 rotations
Track Radius: 73 m

Homework Equations

Average angular velocity = angular displacement/elapsed time

The Attempt at a Solution

Objective for PART B: find angular velocity of the tire

Battle Plan:
Find circumference of track
Find circumference of tire
Find angular displacement (divide circumference of the track by the circumference of the tire)
Divide by elapsed time

Outcome:
73 * 2 * pi = 458.6725274 m
0.33 * 2 *pi = 2.073451151 m
divide the first by the second
221.2121212 rotations
Divide by 850 s
0.260249554 rots/s
0.260249554 rots/s * 2pi = 1.635196274 rad/sWould anyone be willing to tell me what I'm doing wrong here? I know the answer is supposed to be 23 rad/s but I do not see how to get there.

Thank you! (let me know if I can return the favor.)
-Tom

 

[ashishsinghal]

Dividing circumference of the track by the circumference of the tire will not give you anything. You need to find it in the same way as you had done part A. (Here I presume you have done part A correctly as you posted problem with only part B)

 

[Spartan301]

Dividing circumference of the track by the circumference of the tire will not give you anything. You need to find it in the same way as you had done part A. (Here I presume you have done part A correctly as you posted problem with only part B)

Okay I just figured it out. Actually finding the circumferences did help.

I forgot to multiply the circumference of the track by the number of times the bike rotates around it. Once I multiplied the circumference of the track by 14 and did the math I had put together before, it worked!

Thanks for your help and let me know if I can return the favor.