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
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