* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download ExamView - C_Rotation_MC_2008 practice.tst
Sagnac effect wikipedia , lookup
Quantum vacuum thruster wikipedia , lookup
Classical mechanics wikipedia , lookup
Routhian mechanics wikipedia , lookup
Jerk (physics) wikipedia , lookup
Equations of motion wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Old quantum theory wikipedia , lookup
Moment of inertia wikipedia , lookup
Symmetry in quantum mechanics wikipedia , lookup
Laplace–Runge–Lenz vector wikipedia , lookup
Tensor operator wikipedia , lookup
Work (physics) wikipedia , lookup
Centripetal force wikipedia , lookup
Hunting oscillation wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Classical central-force problem wikipedia , lookup
Accretion disk wikipedia , lookup
Rotational spectroscopy wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Photon polarization wikipedia , lookup
Angular momentum wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Name: ________________________ Class: ___________________ Date: __________ ID: A C_Rotation_2008 practice exam Multiple Choice Identify the choice that best completes the statement or answers the question. I) a solid sphere II) a hollow sphere III) a flat disk IV) a hoop 1. Objects I-IV, listed above, have the same mass and radius. They are rolled down a hill. Arrange them in the order they reach bottom. (NOTE: It is possible to reason through this without specific formulas for rotational inertia). A) I, II, III, IV C) IV, II, III, I E) I, IV, III, II B) I, III, II, IV D) IV, III, II, I 2. The angular speed in rad/s of the second hand of a watch is: a) π/1800 A) b) π/60 π π B) 1800 60 c) π/30 C) d) 2π π e) 60 D) 2π 30 E) 60 3. A wheel is spinning at 27 rad/s but is slowing with an acceleration that has a magnitude given by 3t2, in rad/s2 for t in seconds. It stops in a time of: A) 1.7 s B) 2.6 s C) 3.0 s D) 4.4 s E) 7.3 s 4. A wheel rotates with a constant angular acceleration of π rad/s2. During the time interval from t1 to t2 its angular displacement is π radians. At time t2 its angular velocity is 2π rad/s. Its angular velocity in rad/s at time t1 is: A) 0 B) 1 D) π C) π 2 E) π 3 5. String is wrapped around the periphery of a 5.0-cm radius cylinder, free to rotate on its axis. If the string is pulled straight out at a constant rate of 10 cm/s and does not slip on the cylinder, the angular velocity of the cylinder is: C) 10 rad/s E) 50 rad/s D) 25 rad/s A) 2.0 rad/s B) 5.0 rad/s 5.0 N 2.0 m 30o 30o 4.0 m 5.0 N 6. A rod is pivoted about its center. A 5.0 N force is applied 4.0 m from the pivot and another 5.0 N force is applied 2.0 m from the pivot, as shown above. The magnitude of the total torque about the pivot (in Nm) is: 0.0 B) 5.0 C) 8.7 D) 15.0 E) A) L/2 26.0 L/2 7. Three identical objects of mass M are fastened to a massless rod of length L as shown above. The rotational inertia about one end of the rod of this array is: A) ML 2 2 B) ML 2 C) 3ML 2 2 D) 1 5ML 2 4 E) 3ML 2 2 2MR . Assume the earth is a sphere of uniform density. If the period of its rotation is given by T, then 5 its rotational kinetic energy is given by 8. For a solid sphere, I = A) 2MR 2 5 B) 2MR 2 10 C) 4π MR 2 5 D) 2π MR 2 5T E) 4π 2 MR 2 5T 2 9. A grinding wheel, used to sharpen tools, is powered by a motor. A knife held against the wheel exerts a torque of 0.80 N m. If the wheel rotates with a constant angular velocity of 20 rad/s, the work done on the wheel by the motor in 1.0 min is: B) 480 J C) 960 J D) 1400 J E) 1800 J A) 0 10. A hoop (I = MR2) has mass of 200 g and a radius of 25 cm. It rolls without slipping along the ground at 500 cm/s. Its total kinetic energy is: A) 2.5 J B) 5.0 J E) need to know ω C) 10.0 J D) 250 J 4 m/s 6 kg 30o 12 m O 11. A 6-kg particle moves to the right at 4 m/s as shown above. Its angular momentum in kg m2/s2 about point O is: A) 144 B) 240 C) 260 D) 300 E) 388 12. The direction of the angular momentum about point O in the drawing above is: A) Into paper B) Out of paper C) ← D) ↑ E) ↓ 13. An ice skater with rotational inertia I0 is spinning with angular speed ωo. She pulls her arms in, decreasing her rotational inertia to I0/3. Her angular speed becomes: A) ωo 3 B) ωo 3 C) ωo D) 3 ωo E) 3ωo 14. A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms A) his angular velocity increases. D) his rotational kinetic energy increases. B) his angular velocity remains the same. E) his rotational inertia decreases. C) his angular momentum remains the same. 15. A top spinning on the floor precesses because the torque due to gravity, about the point of contact of the top with the floor, is: A) parallel to the angular momentum vector. B) parallel to the angular velocity vector. C) parallel to the axis of rotation. D) perpendicular to the floor. E) parallel to the floor, in the direction of the precession. 16. An asteroid moves in an elliptical orbit with the Sun at one focus. Which of these quantities increases as the asteroid moves from point P in its orbit to point Q? A) speed C) total energy B) angular momentum D) potential energy E) kinetic energy 2 17. Torque is the rotational analog of A) mass C) acceleration B) linear momentum D) force 18. Rotational inertia is the rotational analog of A) mass C) acceleration B) linear momentum D) force E) kinetic energy E) kinetic energy A cylinder rotates with constant angular acceleration about a fixed axis. The cylinder’s moment of inertia about the axis is 4 kg m2. At time t = 0, the cylinder is at rest. At time t = 2 seconds its angular velocity is 1 radian per second. 19. What is the angular acceleration of the cylinder described above between t = 0 and t = 2 second? A) 0.5 rad/s2 B) 1 rad/s2 C) 2 rad/s2 D) 4 rad/s2 E) 5 rad/s2 20. For the cylinder described above, what is the angular momentum of the cylinder at time t = 2 seconds? A) 1 kg m2/s C) 3 kg m2/s E) Need cylinder radius 2 B) 2 kg m /s D) 4 kg m2/s 21. In which direction does the angular momentum point for the front wheel of a bicycle when the bicyclist is traveling due north? A) North B) South C) East D) West E) down 3 ID: A C_Rotation_2008 practice exam Answer Section MULTIPLE CHOICE 1. ANS: B The further from the center the mass is, the higher the rotational inertia and the more energy must go into rotation. That leaves less energy available for translation, and a slower ride down the hill. PTS: 1 DIF: KEY: rotational inertia 2. ANS: C π 2π ω= = 60s 30s moderate REF: 2006 C TOP: conservation of energy with rotation PTS: 1 3. ANS: C Easy REF: 2006 C LOC: angular speed ∫ 0 27 DIF: t t 0 0 ω = ∫ α dt = −∫ 3t 2 dt −27 = − 3t 3 3 t = 3.0s PTS: 1 DIF: Difficult REF: 2006 C TOP: Kinematics KEY: Integral 4. ANS: D This problem is really pretty easy, but the substitution makes it weird. ω22 = ω21 + 2α ∆θ (2π ) 2 = ω21 + 2π (π ) 4π 2 = ω21 + 2π 2 ω21 = 2π 2 ω1 = π 2 PTS: TOP: 5. ANS: v ω= r 1 DIF: Kinematics A 0.10m / s = = 2.0 / s 0.05m PTS: 1 DIF: Moderate to Difficult REF: 2006 C Easy TOP: Angular and Tangential parameters REF: 2006 C 1 ID: A 6. ANS: D Both torques have a common sense (causing rotation in a common direction), and both are applied at an angle of 30o relative to the moment arm. ∑ τ = ∑ rF sin θ = (2m)(5N) sin(30 ) + (4m)(5N) sin(30 ) o o 5 + 10 = 15Nm PTS: 1 DIF: Moderate 7. ANS: D ÊÁ L ˆ˜ 2 5ML 2 I = M ÁÁÁÁ ˜˜˜˜ + ML 2 = 4 Ë2¯ REF: 2006 C TOP: Torque PTS: 1 8. ANS: E REF: 2006 C TOP: Rotational Inerta of point masses REF: 2006 C TOP: Rotational Inertia DIF: K = Iω = 1 2 2 1 2 ÊÁ ˆ ÁÁ 2MR 2 ˜˜˜ ÊÁÁ 2π ÁÁ ˜˜ ÁÁ ÁÁ 5 ˜˜ ÁË T Ë ¯ PTS: 1 9. ANS: C DIF: Easy ˆ˜ 2 4π 2 MR 2 ˜˜ = ˜˜ 5T 2 ¯ Easy The work done by the motor must compensate for the negative work by friction; therefore P= W = τ •ω t W = (τ • ω)t = (0.80)(20)(60) = 960J PTS: 1 DIF: Moderate REF: 3006 C TOP: Power KEY: Torque, angular velocity 10. ANS: B v2 1 1 1 1 K = 2 Iω2 + 2 Mv 2 = 2 MR 2 2 + 2 Mv 2 = MR 2 = (0.200kg)(5.00m / s) 2 = 5.0J R PTS: 1 DIF: Easy to moderate REF: 2006 C TOP: Rotational Kinetic Energy KEY: Rolling without slipping 11. ANS: A l = r × p = rmv sin θ = (12m)(6kg)(4m / s) sin(30) = 144kg ⋅ m / s PTS: KEY: 12. ANS: TOP: 1 DIF: Moderate cross product, magnitude A PTS: 1 Angular momentum REF: 2006 C TOP: Angular Momentum DIF: Easy REF: 2006 C KEY: cross product, direction 2 ID: A 13. ANS: E I 0 ω0 = I 2 ω2 ω2 = I o ωo I o ωo = = 3ωo I2 I0 3 PTS: 1 14. ANS: C DIF: Easy REF: 2006 C TOP: Angular momentum conservation Conservation of angular momentum -- c must be true. (By examination, all others are false) PTS: 1 DIF: KEY: rotational inertia 15. ANS: E Easy REF: 2006 C TOP: Angular momentum conservation The angular momentum vector follows the torque. This is called precession. PTS: 1 DIF: Difficult KEY: Angular momentum, torque 16. ANS: D REF: 2006 C TOP: Precession Further from the sun, and gravitational potential energy rises.c PTS: 1 DIF: Easy KEY: Energy Conservation 17. ANS: D REF: 2006 C TOP: Angular Momentum Conservation Definitional PTS: 1 KEY: Force 18. ANS: A DIF: Easy REF: 2006 C TOP: Torque PTS: 1 KEY: Force 19. ANS: A ∆ω 1 α= = ∆t 2 DIF: Easy REF: 2006 C TOP: Torque PTS: 1 20. ANS: D L = Iω = (4)(1) = 4 DIF: Easy REF: 2006 C TOP: Angular acceleration Definitional PTS: 1 21. ANS: D PTS: 1 TOP: Angular momentum direction DIF: Easy REF: 2006 C KEY: compass directions 3