Question

A motor engine is rotating about its axis with an angular velocity of 100 rev/min, it comes to rest in 15 s, after being switched off. Assuming constant angular deceleration calculate the number of revolutions made by it before coming to rest
A. 10.5
B. 12.5
C. 15
D. 20.5

Answer 1

Hint: This is a problem of rotation and so we can use Newton’s equations in modified form to arrive at our solution. It is given the angular velocity in rev/min, but we know this is not the standard unit, so will modify it accordingly.

Complete step by step answer:
Initial angular velocity, \[{{w}_{0}}=100\]rev/min
\[{{w}_{0}}=\dfrac{100}{60}\]rev/s
Also after 15 s, it comes to rest so its final angular velocity is zero, \[w=0\]
We are given that deceleration is constant, so let us find out using the first equation of motion,
$
w={{w}_{0}}+\alpha t \\
\implies 0=\dfrac{100}{60}+15\alpha \\
\implies 15\alpha =-\dfrac{10}{6} \\
\implies \alpha =-\dfrac{1}{9}rev/{{s}^{2}} \\
$
The value of angular acceleration comes out to be negative as expected. Now we are eager to know the value of the number of revolutions made by it before coming to rest. So, by using the third equation of motion,
$
{{w}^{2}}-w_{0}^{2}=2\alpha \theta \\
\implies 0-{{(\dfrac{5}{3})}^{2}}=-2\times \dfrac{1}{9}\times \theta \\
\therefore \theta =12.5 \\
$

So, the correct answer is “Option b”.

Note:
 here we were given in the question the value of angular velocity in rev/min, always keep in mind the standard SI unit of angular velocity is rev/sec. Also if some question says that the value of angular velocity is /sec, then it does not talk about angular velocity but it talks about frequency and to get angular velocity from frequency we have to use the formula, \[w=2\pi f\].