Question

The linear and angular acceleration of a particle is 10m/sec2 and 5rad/sec2 respectively. It will be at a distance ______ from the axis of rotation.
A. 50m
B. 21​m
C. 1m
D. 2m

Answer 1

Use the relation between linear and angular acceleration.

Formula used: $a=r\alpha$
Here
$a$ is the linear acceleration
$r$ is the distance from the axis of rotation or the radius of the trajectory
$\alpha$ is the angular acceleration

Complete step by step solution:
Given
$\begin{aligned} & a=10\text{m/}{{\text{s}}^{2}} \\\ & \alpha =5\text{rad/}{{\text{s}}^{2}} \\\ \end{aligned}$
Substituting in the formula
$\begin{aligned} & a=r\alpha \\\ & 10=r\times 5 \\\ & r=2\text{m} \\\ \end{aligned}$

The correct answer is option D.

Additional information: There are two types of angular acceleration, spin angular acceleration and orbital angular acceleration. Spin angular acceleration refers to the angular acceleration of a rigid body about its centre of rotation whereas orbital angular acceleration refers to the angular acceleration of a point particle about a fixed origin.
For a rigid body, angular acceleration must be caused by an external torque. In two dimensions it is a pseudoscalar and in three dimensions it is a pseudovector.

Note: Angular acceleration in rotational motion is analogous to linear acceleration in translational motion.