Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS

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1 Accelerated Physics Rotational Dynamics Problem Set Page 1 of 5 Name Date Period PROBLEM SET: ROTATIONAL DYNAMICS Directions: Show all work on a separate piece of paper. Box your final answer. Don t forget to include units. Ignore air resistance unless stated otherwise. Torque 1. Calculate the net torque about the axle of the wheel shown to the right (a) without friction and (b) assuming a friction torque of 0.60 N m opposes the motion. 2. A person exerts a horizontal force of 42.0 N on the end of a door 96.0 cm wide. What is the magnitude of the torque if the force is exerted (a) perpendicular to the door and (b) at a 60.0 angle to the face of the door? 3. You are installing a new spark plug in your car, and the manual specifies that it be tightened to a torque that has a magnitude of 45 N m. Using the data in the drawing, determine the magnitude F of the force that you must exert on the wrench. 4. The bolts on the cylinder head of an engine require tightening to a torque of 95 N m. If a wrench is 28 cm long, what force perpendicular to the wrench must the mechanic exert at its end? If the six-sided bolt head is 15 mm across (figure below), estimate the force applied near each of the six points by a wrench. 5. Determine the net torque on the 2.0-m-long uniform beam shown in the figure to the right. All forces are shown. Calculate about (a) point C, the center of mass and (b) point P at one end. 6. One end of a meterstick is pinned to a table, so the stick can rotate freely in a plane parallel to the tabletop. Two forces, both parallel to the tabletop, are applied to the stick in such a way that the net torque is zero. The first force has a magnitude of 2.00 N and is applied perpendicular to the length of the stick at the free end. The second force has a magnitude of 6.00 N and acts at a 30.0 angle with respect to the length of the stick. Where along the stick is the 6.00-N force applied? Express this distance with respect to the end of the stick that is pinned

2 Accelerated Physics Rotational Dynamics Problem Set Page 2 of 5 Static Equilibrium 7. A uniform meter stick has a 45.0 g mass placed at the 20 cm mark. If a pivot is placed at the 42.5 cm mark and the meter stick remains horizontal in static equilibrium, what is the mass of the meter stick? 8. A meterstick is supported at each side by a spring scale. A heavy mass is then hung on the meterstick so that the spring scale on the left hand side reads four times the value of the spring scale on the right hand side. If the mass of the meterstick is negligible compared to the hanging mass, how far from the right hand side is the large mass hanging? 9. A 5-meter uniform plank of mass 100 kg rests on the top of a building with 2 meters extended over the edge as shown. How far can a 50-kg person venture past the edge of the building on the plank before the plank just begins to tip? 10. A tower crane (figure below) must always be carefully balanced so that there is no net torque tending to tip it. A particular crane at a building site is about to lift a 2800-kg air-conditioning unit. The crane s dimensions are shown in the figure. Ignore the mass of the beam. a. Where must the crane s 9500-kg counterweight be placed when the load is lifted from the ground? b. Determine the maximum load that can be lifted with this counterweight when it is placed at its full extent. 11. A 75.0-kg adult sit at one end of a 9.00-m-long board. His 25.0-kg child sits on the other end. a. Where should the pivot be placed so that the board is balanced, ignoring the board s mass? b. Find the pivot point if the board is uniform and has a mass of 15.0 kg

3 Accelerated Physics Rotational Dynamics Problem Set Page 3 of 5 Rotational Dynamics 12. Determine the moment of inertia of a 10.8-kg sphere of radius m when the axis of rotation is through its center. 13. Estimate the moment of inertia of a bicycle wheel cm in diameter. The rim and tire have a combine mass of kg. The mass of the hub (at the center) can be ignored. 14. A merry-go-round accelerates from rest to 0.68 rad/s in 34 s. Assuming the merry-go-round is a uniform disk of radius 7.0 m and mass 31,000 kg, calculate the net torque required to accelerate it. 15. A grinding wheel is a uniform circular cylinder with a radius of 8.50 cm and a mass of kg. Calculate (a) its moment of inertia about its center and (b) the applied torque needed to accelerate it from rest to 1750 rpm in 5.00 s. (c) Find the applied torque needed for problem (b) taking into account a frictional torque that has been measured to slow down the wheel from 1500 rpm to rest in 55.0 s. 16. The forearm in the figure to the right accelerates a 3.6-kg ball at 7.0 m/s 2 by means of the triceps muscle as shown. Ignoring the mass of the arm, calculate a. the torque needed, and b. the force that must be exerted by the triceps muscle. 17. Suppose David puts a 0.60-kg rock into a sling of length 1.5 m and begins whirling the rock in a nearly horizontal circle, accelerating it from rest to a rate of 75 rpm after 5.0 s. What is the torque required to achieve this feat? 18. A softball player swings a bat, accelerating it from rest to 2.6 rev/s in a time of 0.20 s. Approximate the bat as a 0.90-kg uniform rod of length 0.95 m, and compute the torque the player applies to one end of it. 19. A dad pushes tangentially on a small hand-drive merry-go-round and is able to accelerate it from rest to 15 rpm in 10.0 s. Assume the merry-go-round is a uniform disk of radius 2.5 m and has a mass of 560 kg, and two children (each with a mass of 25 kg) sit opposite each other on the edge. Calculate the torque required to produce the acceleration, neglecting frictional torque. With what (perpendicular) force must the father push? 20. Let us a treat a helicopter rotor blade as a long thin rod, as shown in the figure. a. If each of the three rotor blades is 3.75 m long and has a mass of 135 kg, calculate the moment of inertia of the three rotor blades about the axis of rotation. b. How much torque must the motor apply to bring the blades from rest up to a speed of 6.0 rev/s in 8.0 s?

4 Accelerated Physics Rotational Dynamics Problem Set Page 4 of A centrifuge rotor rotating at 9200 rpm is shut off and is eventually brought uniformly to rest by a frictional torque of 1.20 N m. If the mass of the rotor is 3.10 kg and it can be approximated as a cylinder of radius m, (a) through how many revolutions will the rotor turn before coming to rest, and (b) how long will it take? ,000 More Rotational Dynamics 22. A 15.0-m length of hose is wound around a reel, which is initially at rest. The moment of inertia of the reel is 0.44 kg m2, and its radius is m. When the reel is turning, friction at the axle exerts a torque of magnitude 3.40 N m on the reel. if the hose is pulled so that the tension remains a constant 25.0 N, how long does it take to completely unwind the hose from the reel? Neglect the mass of the hose, and assume that the hose unwinds without slipping. 23. Two blocks are connected by a light string passing over a pulley of radius 0.15 m. The blocks move (toward the right) with an acceleration of 1.00 m/s2 along their frictionless inclines. a. Draw free-body diagrams for each of the two blocks and the pulley. b. Determine the tensions in each of the two parts of the string. c. Find the net torque acting on the pulley. d. Determine the moment of inertia of the pulley. 24. A block (mass = 2.0 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = kg m2), as the figure shows. Initially the pulley is prevented from rotating and box is stationary. Then, the pulley is allowed to rotate as the block falls. The cord does not slip relative to the pulley as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of m during the block s descent. Find the angular acceleration of the pulley and the tension in the cord.

5 Accelerated Physics Rotational Dynamics Problem Set Page 5 of 5 25.By means of a rope whose mass is negligible, two blocks are suspended over a pulley, as the figure shows. The pulley can be treated as a uniform solid cylindrical disk. The downward acceleration of the 44.0-kg block is observed to be exactly one-half the acceleration due to gravity. Noting that the tension in the rope is not the same on each side of the pulley, find the mass of the pulley. 26. Two masses, m A = 65 kg and m B = 75 kg, are connected by a massless inelastic cord that passes over a pulley free to rotate. The pulley is a solid cylinder of radius R = 0.45 m and mass 6.0 kg. a. Determine the acceleration of each mass. b. What % error would be made if the moment of inertia of the pulley is ignored? 27. The radius of the roll of paper shown in the figure below is 7.6 cm and its moment of inertia is I = kg m 2. A force of 3.5 N is exerted on the end of the roll for 1.3 s, but the paper does not tear so it begins to unroll. A constant friction torque of 0.11 N m is exerted on the roll which gradually brings it to a stop. Assuming the the paper s thickness is negligible, calculate: a. the length of paper that unrolls during the time that the force is applied (1.3 s), and b. the length of paper that unrolls from the time the force ends to the time when the roll has stopped moving

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