Physics 106 Sample Common Exam 2, number 2 (Answers on page 6) Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions. Questions 1 through 12 are multiple choice questions worth 5 points each. You may need to do some calculation. Answer each of these on the Scantron sheet using #2 pencil. You may use backs of the question papers for extra space. Questions A and B are work -out problems worth 20 points each. Answer them on the exam booklet and show ALL work, otherwise there is no way to give partial credit. Be sure your name and section number are on both the Scantron form and the exam booklet. Also write your name, Id, and section at the top of each page with long answer questions A and B on them. You may lose points if your name and section number does not appear on each page. Be sure you are in the right room for your section. You may use one side of an 8.5 x 11 sheet or two sides of a 5x8 card as a formula sheet. A default formula sheet is also provided (see page 6 of this booklet). Make sure to bring your own calculator. All cell phones, pagers or similar electronic devices should be turned off. Sharing of calculators is not permitted. Students are not to communicate with each other once the test has started. If you have questions or need something call your proctor or instructor. As you know, NJIT has a zero tolerance policy for ethics code violations during and also after an exam. 1. A bicycle wheel (hoop) rolls without slipping along the floor. The ratio of its translational kinetic energy to its rotational kinetic energy (about an axis through its center of mass) is: A) 1 B) 2 C) 3 D) 1/2 E) 1/3 2. When the speed of a rear wheel drive car is increasing on a horizontal road, the frictional force on the tires is: A) forward for all tires B) backward for all tires C) forward for the front tires and backward for the rear tires D) forward for the rear tires and backward for the front tires E) zero 3. A wheel whose rotational inertia is 10 kg.m 2 starts from rest and accelerates under a constant torque of 3.0 N.m for 8.0 seconds. What is the wheel's rotational kinetic energy at the end of the 8 seconds? A) 28.8 J B) 57.6 J C) 14.4 J D) 64 J E) 128 J 4. A solid ball starts from rest and rolls without slipping down the ramp toward the left as shown in the sketch. The height h = 2 meters. The ball's mass is m and its radius is R. What is the ball's final mass center velocity? A) Can not be determined from the information given B) v cm = sqrt (2gh) C) v cm = sqrt (gh) D) v cm = sqrt (10gh/7) E) v cm = sqrt (5gh/3) v cm h Page of 5 1
5. A single particle is located somewhere on the positive x axis. A net force acting on it points in the negative y direction. The resulting torque points in the: A) positive x direction B) positive y direction C) positive z direction D) negative y direction E) negative z direction 6. Find the cross product A X B when A = 2i + 3j and B = -3i + 2j A) 5j B) zero C) 5i D) 13k E) -5k 7. A 4.0-kg block travels around a 0.50-m radius circle with an angular velocity of 12 rad/s. Its angular momentum about the center of the circle is: A) 12 kg.m 2 /s B) 24 kg.m 2 /s C) 48 kg.m 2 /s D) 6 kg.m 2 /s E) 3 kg.m 2 /s 8. A figure skater goes into a spin, keeping her arms at her sides. When she extends her arms: A) her angular velocity increases. B) her angular velocity remains the same. C) her rotational inertia decreases. D) her rotational kinetic energy increases. E) her angular momentum remains the same. 9. When a star like our sun runs out of nuclear fuel, it collapses to a white dwarf star the size of the Earth, but with the same mass the star had before collapse. If a star initially rotates once every 25 days, like our sun, what will its rotation rate be after it becomes a dwarf? Assume the star is a solid sphere whose initial radius is 7x10 8 m and whose mass is 2x10 30 kg. The Earth's radius is 6.37x10 6 m. A) 4.4 rev/day B) 76.9 rev/day C) 483 rev/day D) 2750 rev/day E) 302,000 rev/day 10. A horizontal disc of rotational inertia 0.01 kg.m 2 and radius 20 cm is rotating about a vertical axis through its center with an angular speed of 4 rad/s. A wad of wet putty of mass 150 grams drops vertically onto the record from above and sticks to the edge of the disk. What is the angular speed of the disk right after the putty sticks to it? A) 1.3 rad/s B) 2.5 rad/s C) 3.3 rad/s D) 4.0 rad/s E) 5.0 rad/s Page of 5 2
11. Two disks are mounted on frictionless bearings on a common shaft. Disc 1 has rotational inertia I 1 and is spinning with angular velocity ω?. Disc 2 has rotational inertia I 2 = 2I 1 and is spinning in the same direction as disc 1 with angular velocity ω 2 = 2ω? as shown. The two disks are slowly forced toward each other along the shaft until they stick together and rotate with a common final angular velocity of: A) 5ω/3 B) ω/sqrt(3) C) 4ω D) ω/3 E) ω/4 I 1 w 1 I 2 w 2 12. If the angular momentum of a system of particles is constant, which of the following statements must be true? A) No torques are acting on any part of the system B) A constant torque acts on every part of the system. C) The net torque is zero on each part of the system D) The net torque is zero for the whole system. E) The net external torque on the system is constant. Show all equations and work for the following problem A). (20 points) A 43.0-kg wheel, essentially a thin hoop of radius 1.50 m, is rotating at 380 rev/min. It must be brought smoothly to a stop in 20.0 s. Calculate the following quantities that are required to achieve this: a) The constant torque on the wheel b) The work done on the wheel to stop it c) The average power. Page of 5 3
Name (Print) 4 Digit ID Section Show all equations and work for the following problem: B) (20 points) A uniform thin rod of length 0.70 m and mass 5.0 kg can rotate in a horizontal plane about a vertical axis through its center. The rod is at rest when a 2.5 g bullet traveling in the horizontal plane of the rod is fired into one end of the rod. As viewed from above, the direction of the bullet's velocity makes an angle of 75 with the rod (see the figure). The bullet lodges in the rod and the angular velocity of the rod is 20 rad/s immediately after the collision. a) What is the bullet's speed just before the impact? 0.70 m M = 5.0 KG 75 o vo m = 2.5 grams b) What is the ratio of the kinetic energy of the entire system after the collision to that of the bullet just before the collision? c) Through what angle will the bullet-thin rod system rotate in 10 s? Page of 5 4
ANSWERS Multiple Choice: 1. A 2. D 3. A 4. D 5. E 6. D 7. A 8. E 9. C 10. B 11. A 12. D Question A: a) -193N.m b) -7.7x10 4 Joules c) 3.8 KW = 3800 Watts Question B: a) 4.7 x 10 3 m/s b) K f /K i = 1.4x10-3 c) 200 radians Page of 5 5