A machinist turns on the power on to a grinding wheel at time t = 0 s. The wheel accelerates uniformly from rest for 10 s and reaches the operating angular speed 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/s? until the wheel stops. What is the tota number of revolutions made by the wheel in this situation? Hint: A multiple part solution. There are three increments of angular displacement: 1) Use A8 = (w+ wo) t. 2) Use A0 = wt. 3) Use w = w? + 2aA0. The angular acceleration is negative since the wheel is slowing down. Remember to convert the total angular displacement in radians to revolutions. O 470 O 280 O 320 O 510 ooo

A turntable (disk) of radius r = 26.0 cm and rotational inertia0.400 kg m2 rotates with an angular speed of 3.00 rad/s arounda frictionless, vertical axle. A wad of clay of mass m =0.250 kg drops onto and sticks to the edge of the turntable.What is the new angular speed of the turntable?

During a 6.0-s time interval, a fly-wheel with a constant angular acceleration turns through 500 radians that acquire an angular velocity of 100 rad/s. (a) What is the angular velocity at the beginning of the 6.0 s? (b) What is the angular acceleration of the fly-wheel?

A bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk (M=0.10kg,R=0.10m) rotating in a horizontal plane around the vertical axis through its center. The disk is rotating at 10.0 rad/s. The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of the disk, what is the angular velocity of the disk then? (d) What is the new kinetic energy of the system? (e) What is the cause of the increase and decrease of kinetic energy?