Question

Angular acceleration of a vehicle is 9 radian/sec^2 where its diameter of wheel is 50cm. Calculate its linear acceleration?​

Answer 1

Given:

Angular acceleration of a vehicle is 9 radian/sec^2 where its diameter of wheel is 50cm.

To find:

Linear acceleration ?

Calculation:

Let angular acceleration be $\alpha$ and linear acceleration be "a", radius be r and diameter be d:

The expression relating angular and linear acceleration is :

$\therefore \: \alpha = \dfrac{a}{r}$

$\implies \: a = \alpha \times r$

$\implies \: a = \alpha \times \dfrac{d}{2}$

$\implies \: a = 9 \times \dfrac{0.5}{2}$

$\implies \: a = 2.25 \: m/ {s}^{2}$

So, linear acceleration of the body is 2.25 m/s².