Question

The motor of an engine is rotating about its axis with an angular velocity of 100 rpm. It comes to rest in 15 sec after being switched off, assuming constant angular deceleration. What is the no. Of revolutions made by it before coming to rest

Answer 1

Explanation:

time =t =15 secs =1`5 /60=1/4 min

angular displacement

θ=[ω+ω0 /2]

t=[0+100/2 X 1/4]

=50/4

=12.5

Answer 2

Given :

• Initial angular velocity = 100 rpm = 10π/3 rad/s
• Final angular velocity = 0
• Time interval = 15 sec

To Find :

• Number of revolution made by motor before coming to rest.

Solution :

Let the angular acceleration be $\alpha$.

Using the equation :

$\tt \omega = \omega_0 + \alpha t \\ \\ \tt \alpha = ( - 2\pi/9)rad/ {s}^{2}$

The angle rotated by the motor during this motion is

$\tt \theta = \omega_0t + \frac{1}{2} a {t}^{2} \\ \\ \tt \implies \bigg( \frac{10\pi}{3} \frac{rad}{s} \bigg)(15 \: s) - \frac{1}{2} \bigg( \frac{2\pi}{9} \frac{rad}{ {s}^{2} } \bigg)(15 {s}^{2} ) \\ \\ \tt \implies25\pi = 12.5$

Hence the motor rotates through 12.5 revolution before coming to rest