Torque and Rotational Acceleration 21. A student gives a quick push to a ball at the end of a massless, rigid rod, causing the ball to rotate clockwise in a horizontal circle. The rod's pivot is frictionless. a. As the student is pushing, is the torque about the pivot positive, negative, or zero? b. After the push has ended, does the ball's angular velocity i. Steadily increase? ii. Increase for awhile, then hold steady? iii. Hold steady? iv. Decrease for awhile, then hold steady? v. Steadily decrease? Explain the reason for your choice. Pivot Push Top View 22. A wheel has a moment of inertia of 3.00 kg m. It is subjected to a 3.50 Nm of torque. What angular acceleration does it experience? 23. A rope is wrapped around a solid cylinder of mass 10 kg with a radius of 1.5 m. What is the angular acceleration of the cylinder if a force of 5.00 N is applied parallel to the edge of the wheel? (I = MR) 24. A 1.53 kg mass hangs on a rope wrapped around a disk-shaped pulley of mass 7.07 kg and radius 66 cm. (I = MR) a. Draw a Free Body Diagram of all the forces on the pulley and the mass below: www.physics.247.com b. What is the linear acceleration of the hanging mass? 17. Consider two solid uniform spheres where both have the same diameter, but one has twice the mass of the other. How much larger is the moment of inertia of the larger sphere compared to that of the smaller sphere? 18. Rank in order, from largest to smallest, the moments of inertia 11, 12, and 13 about the midpoint of each connecting rod. 19. R R/2 2R 12 221 2m m m/2 m/2 2 3 Order: Explanation: A solid cylinder and a cylindrical shell have the same mass, same radius, and turn on frictionless, horizontal axles. (The cylindrical shell has lightweight spokes connecting the shell to the axle.) A rope is wrapped around each cylinder and tied to a block. The blocks have the same mass and are held the same height above the ground. Both blocks are released simultaneously. The ropes do not slip. Which block hits the ground first? Or is it a tie? Explain. 2 20. A board has a mass of 3.5 kg and a total length of 5 meters. a. Calculate the rotational inertia of the board when rotated about the center. (I = 1/12 ML)