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 :

Answer: time(t) = 1.72s

Explanation: [tex]Angular acceleration =\frac{angular velocity}{time taken}[/tex]

Let angular acceleration = α = [tex]2.69rad/s^{2}[/tex]

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, [tex]\frac{44.2 * 2\pi }{60} \\\\ \frac{44.2 * 2*3.142}{60} \\\\= 4.63rads^{-1}[/tex]

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

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