Question

An automobile tire with a radius of 0.30 m starts at rest and accelerates at a constant angular acceleration of 2.0 rad/s2 for 5.0 s. What is the angular displacement of the tire?

Answer 1

The value is
`\theta = 25 \ radian`

Step-by-step explanation:

From the question we are told that

The radius is
`r = 0.30 \ m`

The acceleration is
`\alpha = 2.0 \ rad/s^2`

The time taken is
`t = 5.0`

Generally the angular displacement is mathematically represented as

`\theta = (s)/(r)`

Here s is the linear distance covered by the tire which is mathematically represented as

`s = u t + (1)/(2)a t^2`

Here u is 0 given that the car started from rest and

`a = \alpha * r = 2.0 * 0.30= 0.6\ m/s^2`

So

`s = 0 + (1)/(2)*0.6* 5^2`

`s = 7.5 \ m`

So

`\theta = (7.5)/(0.30)`

=>
`\theta = 25 \ radian`