Question

A clutch plate consists of a flat plate of 40cm in diameter. What is the greatest linear velocity of any point on the clutch plate if it is rotating at 10rev/s about its diameter?
A: $1.26m/s$
B: $12.57m/s$
C: $0.4\pi m/s$
D: $20\pi m/s$

Answer 1

The clutch plate moves or turns in a circular direction about its diameter. In such cases, we can say that the body possesses both linear velocity and angular velocity. The angular velocity is the ratio of the angle covered to the total time taken to cover that angle.
Formula used:
The relation between linear velocity $v$ and angular velocity $\omega$ can be given by
$v=r\omega$, where r is the radius of circular motion.

Complete step by step answer:
Complete step by step answer:
Angular velocity commonly gives the expression of angular displacement over time. It is usually expressed in degrees or radians.
Here, we are given that the clutch plate rotates at a rate of 10rev/s about its diameter.
Since we are given the frequency, we can find the value of angular velocity using the equation
$\begin{aligned} & \omega =2\pi f \\\ & =2\pi \times 10=20\pi \\\ \end{aligned}$
Therefore, the angular velocity is $20\pi$rad/s
Now, we use the relation between linear velocity and angular velocity, that is,
$\begin{aligned} & v=r\omega \\\ & \Rightarrow v=\dfrac{20}{100}\times 20\pi \\\ \end{aligned}$ (Since the diameter is 40cm, radius is 20cm=20/100m)
$\therefore v=4\pi =12.57m/s$
Hence, the greatest linear velocity of the clutch plate at any point is $12.57m/s$

So, the correct answer is “Option B”.

Note:
Angular velocity sensors are devices that are used to measure the rate of rotation of a body with respect to an inertial frame of reference. In general, angular velocity plays an important role in the rotational motion of any body.