Question

A machinist turns on the power on to a grinding wheel at time t = 0s. The wheel accelerates uniformly from rest for 10s and reaches the operating angular speed of 58 rad/s. The wheel is run at that angular velocity for 30s, and then power is shut off. The wheel slows down uniformly at 1.4 rad/s^2 until the wheel stops. What is the total number of revolutions made by the wheel in this situation ? A machinist turns on the power on to a grinding wheel at time t = 0s. The w heel accelerates uniformly from rest for 10s and reaches the operating angular speed of 96 rad/s. The wheel is run at that angular velocity for 40 s and then power is shut off. The wheel slows down uniformly at 1.5 rad/s^2 until the wheel stops. For how long a time after the power is shut off does it take the wheel to stop?

Answer 1

7) wo = 0 , w = 58 rad/s , t = 10 s

from rotationa kinematic equaitons

w = wo + alpha*t

58 = 0 +alpha*10

alpha = 5.8 rad/s^2

w^2-wo^2= 2alpha*theta

58^2 = 2*5.8*theta

theta1 = 290 rad

w = 58 rad/s , t = 30 s

theta = w*t = 58*30

theta2 = 1740 rad

wo = 58 rad/s , alpha = 1.4 rad/s^2

0 - 58^2 = -2*1.4*theta

theta3 = 1201 rad

Theta = theta1+theta2+theta3

= 290+1740+1201 = 3231 rad

theta = 3231/(2*3.14) = 514 rev

8) w = 96 rad/s, wo = 0

alpha = -1.5 rad/s^2

from rotational kinematic equations

w = wo+alpha*t

0 = 96 -1.5*t

t = 64 s