Question

A cyclist traveling at 5m/s uniformly accelerates up to 10 m/s in 2 seconds. Each tire of the bike has a 35 cm radius, and a small pebble is caught in the tread of one of them. (A) What is the angular acceleration of the pebble during those two seconds

Answer 1

`a=2.5\ m/s^2`

Step-by-step explanation:

Given that,

Initial speed, u = 5 m/s

Final speed, v = 10 m/s

Time, t = 2 s

The radius of the tire of the bike, r = 35 cm

We need to find the angular acceleration of the pebble during those two seconds. It can be calculated as follows.

`a=\frac{v-u}t{}\\\\a=(10-5)/(2)\\\\a=2.5\ m/s^2`

So, the required angular acceleration of the pebble is equal to
`2.5\ m/s^2`.