Question

A motor is rotating at a constant angular velocity of 600rpm. The angular displacement in 2 second is ….. rad.

Answer 1

Hint:We are provided with the angular velocity which is constant, hence the angular acceleration of the motor is zero as the velocity is neither decreasing or increasing. Now, first we will find the velocity in terms of radians instead of revolutions and using the relationship of angular displacement with angular velocity, we will find angular displacement with time.

Complete step by step answer:
Here, it is given that the motor is rotating with a constant angular velocity, hence the angular acceleration of the motor would be zero. Letbe the angular acceleration. Thus we have;
\[\alpha = 0\dfrac{{rad}}{{{s^2}}}\]
Let the angular velocity of the motor be denoted as\[\omega \]. Thus, the angular velocity of the motor is follows:
\[\omega = 600rpm\]
The constant angular velocity of the motor in terms of radians and seconds is given as follows:
\[
\omega = 600 \times \dfrac{{2\pi }}{{60}}\dfrac{{rad}}{\operatorname{s} } \\
\omega = 20\pi \dfrac{{rad}}{\operatorname{s} } \\ \]
The motor has been rotating for 2 seconds and we need to find the angular displacement. Let the angular displacement of the motor be denoted by\[\theta \]. Now, we know that the relationship between angular displacement, angular velocity and time is the same as the relation between linear displacement, linear velocity and time. Thus, here, the angular displacement in term of angular velocity and time is given by the relation as follows:
 \[
\Rightarrow \theta = 20 \times 3.14 \times 2 \\
\therefore \theta = 125.6radians \\ \]
Thus the angular displacement is of 125.6 radians.

Note: The displacement here is in terms of radians, which can be converted into rotations. In addition to this, as the angular displacement can be obtained in terms of radians, it can be converted into degrees as well. Thus the angular displacement of any object is dimensionless while the dimensions of angular velocity are $T^{-1}$.