Question

An electric motor rotating a workshop grinding wheel at a rate of 44.2 rev/min is switched off with a constant deceleration of 2.69 rad/s 2 . How long does it take for the grinding wheel to stop?

Answer 1

Answer: time(t) = 1.72s

Explanation:
`Angular acceleration =(angular velocity)/(time taken)`

Let angular acceleration = α =
`2.69rad/s^(2)`

ω = angular velocity = 44rev/ min

the angular velocity is in rev/ min but we need to have it in rad/s , thus we do so below

recall that 1 rev = 2π and 1 min = 60s,
`(44.2 * 2\pi )/(60) \\\\ (44.2 * 2*3.142)/(60) \\\\= 4.63rads^(-1)`

hence 44.2rev/min = 44.2 * 2π/ 60 = 44.2 * 2 *3.142/ 60

thus angular velocity = 4.63rad/s

time taken = angular velocity/ angular acceleration

time taken = 4.63/2.69

time taken = 1.72s