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Download South Pasadena A.P. Physics Name Chapter 8 Rotational Motion
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South Pasadena A.P. Physics Chapter 8 Rotational Motion Name ______________________________ Date ___/___/___ Period ____ “Practice Test” 1. In an effort to tighten a bolt, a force F is applied to a wrench. If the distance from the end of the wrench to the center of the bolt is 20 cm and the applied perpendicular force F = 20 N, what is the magnitude of the torque produced by F? a) 1 m ● N c) 4 m ● N b) 2 m ● N d) 10 m ● N 2. 5. m M A uniform meter stick of mass 1 kg is hanging from a thread attached at the stick’s midpoint. One block of mass m = 3 kg hangs from the left end of the stick, and another block, of unknown mass M, hangs below the 80 cm mark on the meter stick. If the stick remains at rest in the horizontal position as shown above, what is M? 60 L m In the figure above, what is the torque about the pendulum’s suspension point produced by the weight of the bob, given that the length of the pendulum, L is 80 cm and m = 0.50 kg? a) 0.5 m ● N c) 1.7 m ● N b) 1.0 m ● N d) 2.0 m ● N a) 4 kg c) 6 kg b) 5 kg d) 8 kg 6. A carousel a 6FM2 (Six Flags Magic Mountain) accelerates from rest to an angular velocity of 0.3 rad/s in a time of 10 seconds. a) What is the angular acceleration(α)? b) What is the linear acceleration for a point at the outer edge of the carousel, at a radius of 2.5 m from the axis of rotation? 3. Convert 90° to radians 4. Convert 6 radians to degrees 7. How many complete rotations does the carousel make while accelerating to its maximum angular velocity? 8. Calculate the moment of inertia (I) for a bowling ball (solid sphere) with a mass of 10 kg and a radius of 0.2 m. (I = 2/5 mr2) 9. Find the moment of inertia (I) of two 5 kg bowling balls joined by a 1-meter long rod of negligible mass when rotated about the center of the rod. Compare this to the moment of inertia of the object when rotated about one of the masses. (The moment of inertia of each ball will be considered as mr2 since they are not rolling, but rotating. r is not the radius of the ball but the lever arm distance.) CAN YOU GUESS WHICH ONE WILL HAVE A LARGER VALUE? 5 kg 11. Angelina spins on a rotating pedestal with an angular velocity of 8 radians per second. Bob throws her an exercise ball, which increases her moment of inertia from 2 kg ● m2 to 2.5 kg ● m2. What is Angelina’s angular velocity after catching the exercise ball? (Neglect any external torque from the ball.) 12. A 3-kilogram café sign is hung from a 1kilogram horizontal pole as shown in the diagram. A wire is attached to prevent the sign from rotating. Find the tension in the wire. (This problem is similar to the torque hinge lab done in class) 5 kg 30 3m 5 kg 5 kg 10. Gina rolls a bowling ball of mass 7 kg and radius 10.9 cm down a lane with a velocity of 6 m/s. Find the rotational kinetic energy of the bowling ball, assuming it does not slip. (I for a solid sphere is 2/5 mr2) 1m 3 kg 13. Convert 1.5 revolutions to both radians and degrees. 14. A record spins on a phonograph at 33 rpm clockwise. Find the angular velocity, ω, of the record. Let clockwise be the negative direction and counter clockwise be the positive direction. 15. Find the magnitude of the Earth’s angular velocity in radians per second. 16. A frog rides a unicycle that begins at rest, and accelerates uniformly in a counterclockwise direction to an angular velocity of 15 rpm in a time of 6.0 seconds. What is the angular acceleration, , of the unicycle wheel? 17. A knight swings a mace of radius 1 m in two complete revolutions. What is the distance, l, traveled by the mace? 18. A compact disc (CD) player is designed to vary the disc’s rotational velocity so that the point being read by the laser moves at a linear velocity of 1.25 m/s. What is the CD’s rotational velocity in rot/s when the laser is reading information on an inner portion of the disc at a radius of 0.030 m? 19. What is the rotational velocity of the compact disc in the previous problem when the laser is reading the outermost portion of the disc (radius = 0.06 m)? More Torque Problems 20. A captain of a ship takes the helm and turns the wheel of his ship by applying a force of 20 N to the wheel spoke. If he applies the force at a radius of 0.2 m from the axis of rotation, at an angle of 80° to the line of action, what torque does he apply to the wheel? 21. A mechanic tightens the lugs on a tire by applying a torque of 110 m-N at an angle of 90° to the line of action. What force is applied if the wrench is 0.4 meters long? 22. What is the minimum length of the wrench if the mechanic is only capable of applying a force of 200 N? 23. A variety of masses are attached at different point to a uniform beam attached to a pivot. Rank the angular accelerations (α) of the beam from largest to smallest. A • 2M B • 3M C D • 2M M M 2M • 24. A 10-kg tortoise sits on a see-saw 1 meter from the fulcrum. Where must a 2-kg hare (rabbit) sit in order to maintain rotational equilibrium? Assume the see-saw is massless. (First Draw a Diagram) 28. An object with uniform mass density is rotated about an axle, which may be in position A, B, C, or D. Rank the object’s moment of inertia from smallest to largest based on axle position. D • • Moment of Inertia (or Rotational Inertia) 25. Calculate the moment of inertia for a hollow sphere with a mass of 10 kg and a radius of 0.2 m. Compare this answer to the answer to question #8. (Look up the formula for a hollow sphere in your textbook.) 26. Calculate the moment of inertia for a long thin rod with a mass of 2 kg and a length of 1 m rotating around the center of its length. (Look up the formula for a long thin rod in your textbook.) 27. Calculate the moment of inertia for a long thin rod with a mass of 2 kg and a length of 1 m rotating about its end. (Look up the formula in your textbook.) How does this answer compare to the previous answer in #26? C A • • B 29. What is the angular acceleration experienced by a uniform solid disc of mass 2-kg and radius 0.1 m when a net torque of 10 m•N is applied? Assume the disc spins about its center. (Hint: Just as Fnet = ma τnet = I α) and Idisc = ½ mr2) 30. A merry-go-round on a playground with a moment of inertia of 100 kg•m2 starts at rest and is accelerated by a force of 150 N at a radius of 1 m from its center. If this force is applied at an angle of 90° from the line of action for a time of 0.5 seconds, what is the final rotational velocity, ω, of the merry-goround? Hint: First find torque, τ, then find α, then find ω. Answers: 12. First show all of the forces on the pole as a means to illustrate the various torques. Assume the pivot is the attachment point on the left hand side of the pole. 1. c) 2. d) There are two torques acting downward or clockwise and one torque acting upwards or counterclockwise. The sum of these three torques is zero since the pole is in equilibrium. (g = 9.8 m/s2) 3. 1.57 rad 4. 344 ° 5. b) 6. α = 0.3 rad/s = 0.03 rad/s2 10 s and a =r = 0.075 m/s2 τ net = τ up – τ1 down − τ2 down = T sin 30 (4m) – (3 kg)(g)(3 m) – (1 kg) (g) (2 m) = 0 7. = ½ α t2 = 1.5 radians T = 11 kg ● m x g = 54 N 4 m sin 30 1.5 radians x 1rot/2πradians = 0.24 rotations 13. 9.42 radians and 540° 14. ‒ 3.46 rad/s 15. 7.27 x 10‒5 rad/s 16. 1.57 rad/s and 0.26 rad/s2 9. I = Σ mr2 = (5 kg)(0.5 m)2 + (5 kg)(0.5 m)2 = 2.5 kg ● m2 17. l = r θ = 12.6 m 18. ω = v/r = 41.7 rad/s = 6.63 rot/s I = Σ mr2 = (5 kg)(1m)2 + (5 kg)(0 m)2 = 5.0 kg ● m2 19. 20.8 rad/s and 3.32 rot/s 20. τ = r F sin θ = 3.94 m•N 21. 275 N 22. 0.55 m 23. D, C, A, B 24. 5 m from fulcrum 25. 0.27 kg ● m2 = ½ (0.0333 kg ● m2) (55 rad/s)2 26. 0.17 kg ● m2 = 50.4 Joules 27. 0.67 kg ● m2 28. C, B, D, A 29. 1,000 rad/s2 30. τ = 150 m•N and α = 1.5 rad/s2 and ω = 0.75 rad/s 8. I = 0.16 kg ● m2 10. I = 2/5 mr2 = 2/5 (7 kg) ((0.109 m)2 = 0.0333 kg ● m2 ω = v/r = 6 m/s / 0.109 m = 55 rad/second K.E. rot = ½ I ω2 11. L0 = L or I0 ω0 = I ω ω = I0 ω0 = (2.0 kg ● m2) (8 rad/s) I 2.5 kg ● m2 = 6.4 rad/s