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1 Use the following to answer question 1: On an amusement park ride, passengers are seated in a horizontal circle of radius 7.5 m. The seats begin from rest and are uniformly accelerated for 21 seconds to a maximum rotational speed of 1.4 rad/s. 1. What is the instantaneous tangential speed of the passengers 15 s after the acceleration begins? A) m/s B) 0.50 m/s C) 1.4 m/s D) 7.5 m/s E) 11 m/s 2. A rigid body rotates about a fixed axis with a constant angular acceleration. Which one of the following statements is true concerning the tangential acceleration of any point on the body? A) The tangential acceleration is zero m/s 2. B) The tangential acceleration depends on the angular velocity. C) The tangential acceleration is equal to the centripetal acceleration. D) The tangential acceleration is constant in both magnitude and direction. E) The tangential acceleration depends on the change in the angular velocity. 3. A ball attached to a string starts at rest and undergoes a constant angular acceleration as it travels in a horizontal circle of radius 0.30 m. After 0.65 sec, the angular speed of the ball is 9.7 rad/s. What is the tangential acceleration of the ball? A) 4.5 m/s 2 B) 0.32 m/s 2 C) 15 m/s 2 D) 7.6 m/s 2 E) 28 m/s 2 4. A bicycle wheel of radius 0.70 m is rotating at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel? A) 1.4 m/s B) 28 m/s C) 0.11 m/s D) 4.4 m/s E) 9.1 m/s Page 1

2 Use the following to answer question 5: A long thin rod of length 2L rotates with a constant angular acceleration of 8.0 rad/s 2 about an axis that is perpendicular to the rod and passes through its center. 5. What is the ratio of the angular speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4 6. A fan rotating with an initial angular velocity of 1000 rev/min is switched off. In 2 seconds, the angular velocity decreases to 200 rev/min. Assuming the angular acceleration is constant, how many revolutions does the blade undergo during this time? A) 10 B) 20 C) 100 D) 125 E) A grindstone, initially at rest, is given a constant angular acceleration so that it makes 20.0 rev in the first 8.00 s. What is its angular acceleration? A) rad/s 2 B) rad/s 2 C) 2.50 rad/s 2 D) 1.97 rad/s 2 E) 3.93 rad/s 2 Page 2

3 Use the following to answer question 8: An 80-kg man balances the boy on a teeter-totter as shown. Note: Ignore the weight of the board. 8. What, approximately, is the magnitude of the downward force exerted on the fulcrum? A) zero newtons B) 100 N C) 600 N D) 800 N E) 1000 N 9. Three objects are positioned along the x axis as follows: 4.4 kg at x = m, 3.7 kg at x = 0.80 m, and 2.9 kg at x = 1.6 m. The acceleration due to gravity is the same everywhere. What is the distance from the location of the center of gravity to the location of the center of mass for this system? A) zero meters B) 0.52 m C) 0.26 m D) m E) m Page 3

4 10. A massless frame in the shape of a square with 2-m sides has a 1-kg ball at each corner. What is the moment of inertia of the four balls about an axis through the corner marked O and perpendicular to the plane of the paper? A) 4 kg m 2 B) 8 kg m 2 C) 10 kg m 2 D) 12 kg m 2 E) 16 kg m A 45-N brick is suspended by a light string from a 2.0-kg pulley. The brick is released from rest and falls to the floor below as the pulley rotates through 5.0 rad. The pulley may be considered a solid disk of radius 1.5 m. What is the angular speed of the pulley? A) 17 rad/s B) 15 rad/s C) 9.4 rad/s D) 8.1 rad/s E) 7.3 rad/s Page 4

5 12. A child standing on the edge of a freely spinning merry-go-round moves quickly to the center. Which one of the following statements is necessarily true concerning this event and why? A) The angular speed of the system decreases because the moment of inertia of the system has increased. B) The angular speed of the system increases because the moment of inertia of the system has increased. C) The angular speed of the system decreases because the moment of inertia of the system has decreased. D) The angular speed of the system increases because the moment of inertia of the system has decreased. E) The angular speed of the system remains the same because the net torque on the merry-go-round is zero N m. 13. A uniform disk of radius 1.2 m and mass 0.60 kg is rotating at 25 rad/s around an axis that passes through its center and is perpendicular to the disk. A rod makes contact with the rotating disk with a force of 4.5 N at a point 0.75 m from the axis of rotation as shown. The disk is brought to a stop in 5.0 s. What is the coefficient of kinetic friction for the two materials in contact? A) 0.22 B) 0.15 C) 0.64 D) 0.37 E) A string is wrapped around a pulley of radius 0.20 m and moment of inertia 0.40 kg m 2. The string is pulled with a force of 28 N. What is the magnitude of the resulting angular acceleration of the pulley? A) 22 rad/s 2 B) 14 rad/s 2 C) 68 rad/s 2 D) 0.55 rad/s 2 E) 8.0 rad/s 2 Page 5

6 15. When a force of 19 N is applied to a spring, it elongates m. Determine the period of oscillation of a 4.0-kg object suspended from this spring. A) 0.8 s B) 1.2 s C) 3.1 s D) 4.1 s E) 6.3 s 16. A spring required a force of 5.0 N to compress it 0.1 m. How much work is required to stretch the spring 0.4 m? A) 0.4 J B) 0.6 J C) 0.8 J D) 2 J E) 4 J 17. The spring constant for the spring in a special cannon is 1800 N/m. In cocking the cannon, the spring is compressed 0.55 m. What is the initial speed of a 7.0-kg cannonball at rest on the free end of the spring when it is released? A) 77 m/s B) 140 m/s C) 12 m/s D) 8.8 m/s E) 16 m/s 18. Young's modulus of nylon is N/m 2. A force of N is applied to a 1.5-m length of nylon of cross sectional area 0.25 m 2. By what amount does the nylon stretch? A) m B) m C) m D) m E) m Page 6

7 19. A spring with constant k = 78 N/m is at the base of a frictionless, inclined plane. A 0.50-kg block is pressed against the spring, compressing it 0.20 m from its equilibrium position. The block is then released. If the block is not attached to the spring, how far up the incline will it travel before it stops? A) m B) 0.16 m C) 0.32 m D) 0.64 m E) 1.1 m 20. A kg object hanging from a vertical spring is observed to oscillate with a period of 1.50 s. When the kg object is removed and replaced by a 1.50-kg object, what will be the period of oscillation? A) 1.55 s B) 2.58 s C) 2.12 s D) 3.38 s E) 4.49 s Page 7

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