gets from rest at tref and rotates with an angular given by off)4.0 where is in seconds and is in rad What is the angular acceleration at 1-40 seconds? C. 20 A Omda 8-12.0 rad D-16 d The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods, as indicated. Which rod expenances the greatest magnitude gravitational torque? A 0,5 10 15 2.0 B. T 0.5 1.0 1.3 2.0 . T 0.5 1.0 1.5 2.0 D. . 03 1.0 1.5 2.0 8. E 0 0.5 1.0 1.5 2.0 A uniform rod is 2.1 m long. It is hinged to a wall at its left end, and held in a horizontal position at its right end by a vertical very light string, as shown in the figure. What is the angular acceleration of the rod at the moment after the string is released if there is no friction in the hinge? A. 7.0 rad's B. 14.0 rad/sC. 3.3 rad/s D. 28 rad/s E it cannot be calculated without knowing the mass of the rod. Hinge Rod Wall String A uniform rod is 3.0 m long and has a mass of 0.25 kg. The rod is pivoted about a horizontal, frictionless pin through one end. The rod is released from rest at an angle of 27" above the horizontal. What is the kinetic energy of the rod as it passes through the horizontal position? A. 3.38 J B.2.34 J C. 4.34 J D. 2.94 J E. 1.67 J (Hint: use the right-hand rule) The object shown below has mass m and velocity V. The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is A. downwards B. into the page C. out of the page D. to the right 10. A small mass is whirled in a horizontal circle at the end of a light string 75 cm long at a speed of 3.0 m/s. If the string is lengthened to 1.5 m while still in motion, then the ball will have? A. Smaller speed and larger angular momentum. B. Larger speed and larger angular momentum. C. Smaller speed and smaller angular momentum. D. Smaller speed and the same angular momentum. MCD SETUP ON log-l nd rotates with an angular displacement given by 0(t) = 4.01 -0. eleration at 14.0 seconds? -16 rad/s axes through the SHORT ANSWER: Show work on separate paper to support your answers and answers with no work shown may not receive full credit. receive partial credit. Circle your final answers and be sure to include units. Correct 3, 11. (8 pts.) The cue ball in billiards has a mass of 0.120 kg and moves with a speed of 6.0 m/s and strikes the 8-ball, initially at rest. The mass of the 8-ball is 0.123 kg. As a result of the collision, the cue ball is deflected off at 24 above the horizontal with a velocity of 4.0 m/s as shown, Calculate the velocity (magnitude and direction) of the 8-ball after the collision. Vi 24 8 12. (9 pts.) A wheel rotating about a fixed axis with a constant angular acceleration of 2.0 rad/s starts from rest at t= 0. The wheel has a diameter of 20 cm. What is the magnitude of the total linear acceleration of a point on the outer edge of the wheel at t = 0.60 s? 13. (10 pts.) A mass (M = 5.0 kg) is connected by a light cord to a mass (M2 = 4.0 kg) which slides on a smooth surface, as shown in the figure. The pulley (radius = 0.20 m) rotates about a frictionless axle. The acceleration of M2 is 3.5 m/s. What is the moment of inertia of the pulley? M M1 14. (8 pts.) A skater extends her arms horizontally, holding a 5-kg mass in each hand. She is rotating about a vertical axis with an angular velocity of one revolution per second. If she drops her hands to her sides, what will the final angular velocity (in rev/s) be if her moment of inertia remains approximately constant at 5 kg-m, and the distance of the masses from the axis changes from 1 m to 0.1 m? 15. (6 pts.) A horizontal, uniform 1.20-N meter stick is held up by two vertical strings, one at the 20-cm mark and the other at the 60-cm mark. a) Draw the free-body diagram for this situation. Include an axis of rotation. b) State the sum of forces for equilibrium. State the sum of torques for equilibrium. c) What is the tension in the string at the 60-cm mark?