
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. 21m
C. 1m
D. 2m
Answer
497.4k+ views
Hint: 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
$\begin{align}
& a=10\text{m/}{{\text{s}}^{2}} \\
& \alpha =5\text{rad/}{{\text{s}}^{2}} \\
\end{align}$
Substituting in the formula
$\begin{align}
& a=r\alpha \\
& 10=r\times 5 \\
& r=2\text{m} \\
\end{align}$
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.
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
$\begin{align}
& a=10\text{m/}{{\text{s}}^{2}} \\
& \alpha =5\text{rad/}{{\text{s}}^{2}} \\
\end{align}$
Substituting in the formula
$\begin{align}
& a=r\alpha \\
& 10=r\times 5 \\
& r=2\text{m} \\
\end{align}$
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.
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