The motor of an engine is rotating about its axis with an angular velcoity of `100 rev me^(-1)` . It comes to rest is 15 s, after being switched off. Assuming constant angualar decelearation . What are the numbers of revolutions made by it befor coming to rest ?

Options

A. 12.5
B. 40
C. 32.6
D. 15.6

Answer

A

Explanation

From equation of motion ,
` 0 - omega_(0) - alpha t rArr alpha = (omega_(0))/(t)`
` = ((100 xx 2pi)//60)/(15) = 0.7 rad s^(-2)`
Now angle rotated befor coming to rest
` theta = (omega_(0)^(2))/(2 alpha) = (((100 xx2pi)/(60))^(2))/(2 xx 0.7) = 78.25 rad s^(-2)`
Number of rotations , `n = (theta)/(2pi) (78.25)/(2 xx 3.14) = 12.5`