Question

A bicycle wheel has a small pebble embedded in its tread. The bike is set upside down, and the rider accidentally bumps the wheel and the pebble moves through an arc length of 25.0 cm before coming to rest. In that time, the wheel spins 35°. (a) The radius of the wheel is therefore (1) more than 25.0 cm, (2) less than 25.0 cm, or (3) equal to 25.0 cm. (b) Determine the radius of the wheel.

Answer 1

a) The radius of the wheel is 1) more than 25.0 cm.

b) The radius of the wheel is approximately 40.925556... cm

Explanation:

S = rθ is the formula to find the radius of the wheel using the arc and the angle discovered, S being the arc and θ the angle. The angle, however, must be in radians. θ =
`(35\pi)/(180)` is used to convert it. So:

θ =
`(35\pi)/(180)`

θ =
`(7\pi)/(36)`

S = rθ

25 = r
`(7\pi)/(36)`

900 = 7
`\pi`r

r =
`(900)/(7\pi )`

r = 40.925556... cm