SECTION A Torque and Statics

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1 AP Physics C Multiple Choice Practice Rotation SECTON A Torque and Statics 1. A square piece o plywood on a horizontal tabletop is subjected to the two horizontal orces shown above. Where should a third orce o manitude 5 newtons be applied to put the piece o plywood into equilibrium?. A uniorm riid bar o weiht W is supported in a horizontal orientation as shown above by a rope that makes a 30 anle with the horizontal. The orce exerted on the bar at point O, where it is pivoted, is best represented by a vector whose direction is which o the ollowin? (B) (E) 3. A rod o neliible mass is pivoted at a point that is o-center, so that lenth l 1 is dierent rom lenth l. The iures above show two cases in which masses are suspended rom the ends o the rod. n each case the unknown mass m is balanced by a known mass, M 1 or M, so that the rod remains horizontal. What is the value o m in terms o the known masses? M l + M (B) ½(M l + M ) M l M M M 1

2 4. A system o two wheels ixed to each other is ree to rotate about a rictionless axis throuh the common center o the wheels and perpendicular to the pae. Four orces are exerted tanentially to the rims o the wheels, as shown above. The manitude o the net torque on the system about the axis is FR (B) FR 5FR 14FR 5. For the wheel-and-axle system shown above, which o the ollowin expresses the condition required or the system to be in static equilibrium? m 1 = m (B) am 1 = bm am = bm 1 a m l = b m

3 SECTON B Rotational Kinematics and Dynamics 1. A uniorm stick has lenth L. The moment o inertia about the center o the stick is o. A particle o mass M is attached to one end o the stick. The moment o inertia o the combined system about the center o the stick is 1 1 ML (B) 3 ML ML ML 4 4. A liht riid rod with masses attached to its ends is pivoted about a horizontal axis as shown above. When released rom rest in a horizontal orientation, the rod beins to rotate with an anular acceleration o manitude 5 7 l (B) 5 l 4 l 7l 3. n which o the ollowin diarams is the torque about point O equal in manitude to the torque about point X in the diaram above? (All orces lie in the plane o the paper.) Questions 4-5 An ant o mass m clins to the rim o a lywheel o radius r, as shown above. The lywheel rotates clockwise on a horizontal shat S with constant anular velocity. As the wheel rotates, the ant revolves past the stationary points,,, and V. The ant can adhere to the wheel with a orce much reater than its own weiht. 4. t will be most diicult or the ant to adhere to the wheel as it revolves past which o the our points? (B) V 5. What is the manitude o the minimum adhesion orce necessary or the ant to stay on the lywheel at point? m (B) m r m r - m m r + m

4 6. A turntable that is initially at rest is set in motion with a constant anular acceleration. What is the anular velocity o the turntable ater it has made one complete revolution? (B) 4 4 Questions 7-8 A wheel with rotational inertia is mounted on a ixed, rictionless axle. The anular speed o the wheel is increased rom zero to in a time interval T. 11. What is the averae net torque on the wheel durin this time interval? (B) T T T T 1. What is the averae power input to the wheel durin this time interval? (B) T T T T 9. Two blocks are joined by a liht strin that passes over the pulley shown above, which has radius R and moment o inertia about its center. T 1 and T are the tensions in the strin on either side o the pulley and α is the anular acceleration o the pulley. Which o the ollowin equations best describes the pulley's rotational motion durin the time the blocks accelerate? m R = α (B) T R = α (T - T 1)R = α (m m 1)R = α Questions A solid cylinder o mass m and radius R has a strin wound around it. A person holdin the strin pulls it vertically upward, as shown above, such that the cylinder is suspended in midair or a brie time interval t and its center o mass does not move. The tension in the strin is T, and the rotational inertia o the cylinder about its axis is 1 MR 10. the net orce on the cylinder durin the time interval t is m (B) T mr mr - Τ zero 11. The linear acceleration o the person's hand durin the time interval t is T - m (B) T m m

5 1. A block o mass m is placed aainst the inner wall o a hollow cylinder o radius R that rotates about a vertical axis with a constant anular velocity ω, as shown above. n order or riction to prevent the mass rom slidin down the wall, the coeicient o static riction μ between the mass and the wall must satisy which o the ollowin inequalities? µ ³ w R (B) µ ³ w R SECTON C Rollin µ w R µ w R 1. A bowlin ball o mass M and radius R. whose moment o inertia about its center is (/5)MR, rolls without slippin alon a level surace at speed v. The maximum vertical heiht to which it can roll i it ascends an incline is v 5 Questions -3 (B) v 5 v 7v 10 A sphere o mass M, radius r, and rotational inertia is released rom rest at the top o an inclined plane o heiht h as shown above.. the plane is rictionless, what is the speed v cm, o the center o mass o the sphere at the bottom o the incline? h (B) Mhr Mhr Mhr Mr 3. the plane has riction so that the sphere rolls without slippin, what is the speed v cm o the center o mass at the bottom o the incline? h (B) Mhr Mhr Mhr Mr 4. A car travels orward with constant velocity. t oes over a small stone, which ets stuck in the roove o a tire. The initial acceleration o the stone, as it leaves the surace o the road, is vertically upward (B) horizontally orward horizontally backward upward and orward, at approximately 45 to the horizontal

6 SECTON D Anular Momentum 1. An ice skater is spinnin about a vertical axis with arms ully extended. the arms are pulled in closer to the body, in which o the ollowin ways are the anular momentum and kinetic enery o the skater aected? Anular Momentum Kinetic Enery ncreases ncreases (B) ncreases Remains Constant Remains Constant ncreases Remains Constant Remains Constant. A particle o mass m moves with a constant speed v alon the dashed line y = a. When the x-coordinate o the particle is x o, the manitude o the anular momentum o the particle with respect to the oriin o the system is zero (B) mva mvx o mv x a 0 3. The riid body shown in the diaram above consists o a vertical support post and two horizontal crossbars with spheres attached. The masses o the spheres and the lenths o the crossbars are indicated in the diaram. The body rotates about a vertical axis alon the support post with constant anular speed. the masses o the support post and the crossbars are neliible, what is the ratio o the anular momentum o the two upper spheres to that o the two lower spheres? /1 (B) 1/ 1/4 1/8 4. A lon board is ree to slide on a sheet o rictionless ice. As shown in the top view above, a skater skates to the board and hops onto one end, causin the board to slide and rotate. n this situation, which o the ollowin occurs? Linear momentum is converted to anular momentum. (B) Rotational kinetic enery is conserved. Translational kinetic enery is conserved. Linear momentum and anular momentum are both conserved.

7 Top View 5. Multiple Correct. A disk slidin on a horizontal surace that has neliible riction collides with a rod that is ree to move and rotate on the surace, as shown in the top view above. Which o the ollowin quantities must be the same or the disk-rod system beore and ater the collision? Select two answers.. Linear momentum. Anular momentum. Kinetic enery Linear Momentum (B) Anular Momentum Kinetic Enery Mechanical Enery

AP Physics QUIZ Chapters 10

AP Physics QUIZ Chapters 10 Name: 1. Torque is the rotational analogue of (A) Kinetic Energy (B) Linear Momentum (C) Acceleration (D) Force (E) Mass A 5-kilogram sphere is connected to a 10-kilogram sphere by a rigid rod of negligible