Question

A scooter is going round a circular road of radius 100 m at a speed of \[10\,m{s^{ - 1}}\]. Find the angular speed of the scooter.
A. \[0.01\,rad{s^{ - 1}}\]
B. \[0.1\,rad{s^{ - 1}}\]
C. \[1\,rad{s^{ - 1}}\]
D. \[10\,rad{s^{ - 1}}\]

Answer 1

Hint:Before we start addressing the problem, we need to know about angular speed. Angular speed is defined as the speed of the object in rotational motion. Here, the distance travelled is represented as\[\omega \]and is measured in radians. The time taken is measured in terms of seconds. Therefore, the unit of angular speed is radians per second.

Formula Used:
The relation between linear and angular velocity is,
\[v = r\omega \]
Where, r is radius, v is the linear velocity and \[\omega \] is the angular velocity.

Complete step by step solution:
Consider a scooter that is moving in the round on a circular road of a radius of 100m at a speed of \[10\,m{s^{ - 1}}\]. We need to find the angular speed of the scooter. In order to find the angular speed of a scooter, we have the relation between the linear and angular velocity (speed) that is given by,
\[v = r\omega \]

Substitute the value of \[r = 100\,m\] and \[v = 10\,m{s^{ - 1}}\] then the above equation will become,
\[\omega = \dfrac{v}{r}\]
\[\Rightarrow \omega = \dfrac{{10}}{{100}}\]
\[\therefore \omega = 0.1\,rad{s^{ - 1}}\]
Therefore, the angular speed of the scooter is \[0.1\,rad{s^{ - 1}}\].

Hence, Option B is the correct answer

Note:In this problem it is important to remember the difference between the angular speed and the angular velocity. The angular speed is a scalar quantity that measures the speed of a rotating object and angular velocity is a vector quantity that measures the speed of a rotating object. Angular speed specifies only the magnitude. Angular velocity specifies both magnitude and direction but the unit of both speed and velocity is the same that is \[m{s^{ - 1}}\].