Question

A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 58 rad/s. The wheel is run at that angular velocity for 30 s and then power is shut off. The wheel slows down uniformly at 1.4 rad/s2 until the wheel stops. In this situation, the total number of revolutions made by the wheel is closest to:

Answer 1

Ф=1716.8 Rev

Step-by-step explanation:

A machinist turns the power on to a grinding wheel, at rest, at time t = 0 s. The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 58 rad/s. The wheel is run at that angular velocity for 30 s and then power is shut off. The wheel slows down uniformly at 1.4 rad/s2 until the wheel stops. In this situation, the total number of revolutions made by the wheel is closest to:

the time it takes to stop revolution will be found using this using this equation

ω2=final angular velocity

ω1=initial angular velocity

∝=angular deceleration

t=time

ω2=ω1+∝t

0=58 rad/s-1.4 rad/s^2t

t=58/1.4

t=39.28secs

to get the total number of revolution made by the wheel ,we get the area under the graph, which is a trapezium

Ф=1/2(20+39.2)*58

Ф=1716.8 Rev

Answer 2

The total number of revolutions made by the wheel is closest to is 28.2 revolutions. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.