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Exam 3 is at 7 pm tomorrow Conflict is at 5:15 pm in 151 Loomis There are extra office hours today & tomorrow This morning’s HW deadline moved to Friday (80% deadline not moved – still next Tuesday) A ladder of weight 60 N leans against a frictionless wall at an angle of q = 70o as shown in the figure. Friction between the floor and the ladder keeps it from slipping . What is the magnitude of the force of friction, Ff, between the floor and the ladder? a. b. c. d. e. Ff = 5.0 N Ff = 11. N Ff = 15. N Ff = 29. N Ff = 60 N 2. If the angle of the ladder were decreased from 70o to 50o, the force of friction required to keep the ladder from slipping would a. increase b. decrease c. remain the same Consider a student rotating on a stool with angular speed , holding weights in her outstretched hands. If she drops one of the weights to the ground, her angular speed will a. increase b. stay the same c. decrease 4. Now consider a student rotating on a stool with angular speed with no weights in her hands. Suppose someone drops (vertically) a small weight into her horizontally outstretched hand. Her angular speed will a. increase b. stay the same c. decrease A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely about a pivot at its center. The gum sticks to the end of the bar and the angular speed of the bar just after the collision is measured to be = 3 rad/s. Assume that the wad of gum is a point particle and assume that the pivot is frictionless. (You do not have to worry about gravity in this problem) 5. What is the magnitude of the angular momentum of the gum with respect to the pivot before it collides with the bar? a. 0 kg m2 /s b. 0.48 kg m2 /s c. 1.12 kg m2 /s A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely about a pivot at its center. The gum sticks to the end of the bar and the angular speed of the bar just after the collision is measured to be = 3 rad/s. Assume that the wad of gum is a point particle and assume that the pivot is frictionless. (You do not have to worry about gravity in this problem) 6. What is the angular momentum of the gum with respect to the pivot after it collides with bar? a. 0.29 kg m2 /s b. 0.48 kg m2 /s c. 1.12 kg m2 /s A wad of gum having mass m = 0.2 kg is thrown with speed v=8 m/s at a perpendicular bar with length d = 1.4 m and mass M. The bar is initially at rest but can rotate freely about a pivot at its center. The gum sticks to the end of the bar and the angular speed of the bar just after the collision is measured to be = 3 rad/s. Assume that the wad of gum is a point particle and assume that the pivot is frictionless. (You do not have to worry about gravity in this problem) 7. What is the mass of the bar? a. b. c. d. e. 1.7 kg 2.0 kg 2.3 kg 3.1 kg 5.2 kg The axle of a spinning disk of mass m is placed upon a single fixed support as shown below. The disk’s angular velocity vector is indicated in the figure, as is the gravitational force on the disk. L pivot mg 8. Which of the following figures accurately shows the motion of the spinning disk? a. As viewed from above, the disk precesses clockwise: pivot mg b. As viewed from above, the disk precesses counter-clockwise. pivot mg c. The disk does not fall and does not precess. pivot mg A skater spins about a fixed point on the ice. She begins with her arms extended and an initial angular velocity 0. She then pulls her arms in to her body. After her arms are pulled to her body, she spins with an angular velocity f. Throughout the time she is spinning, no external forces are acting in the horizontal plane. 9. How do the magnitudes of the initial and final angular velocities compare? a. 0 > f b. 0 = f c. 0 < f 10. Which one of the following statements is true? a. The angular momentum of the skater remains constant. b. The moment of inertia of the skater remains constant. c. Both the angular momentum and the moment of inertia of the skater change. 11. The kinetic energy of the skater a. increases because the skater does work. b. decreases because the skater does work. c. stays the same because the skater does no work. A uniform rod of mass M = 2 kg and length L = 1.5 m is attached to a wall with a frictionless pivot and a string as shown in the diagram above. The initial angle of the rod with respect to the wall, , is 39. The string is then cut. The moment of inertia of a rod about an axis through one end is 1/3ML2. 12. What is the angular acceleration of the rod, , immediately after the string is cut? a. b. c. d. e. = 1.75 rad/s2 = 3.09 rad/s2 = 4.92 rad/s2 = 6.17 rad/s2 = 7.84 rad/s2 13. What is the angular velocity of the rod when it is horizontal (=90) a. 1.4 rad/sec b. 3.1 rad/sec c. 3.9 rad/sec A disk of radius R, mass M, and moment of inertia I = (1/2)MR2 rolls without slipping down an incline and onto a horizontal table. The disk then continues to the right and goes up a frictionless ramp. The disk starts at rest at a height h above the table, as shown 14. What is the speed of the center of mass of the disk when it reaches the bottom of the ramp? a. b. c. 2 gh 4 gh 3 10 gh 7 d. gh e. Mgh 15. What is the maximum height above the table that the disk reaches on the frictionless ramp? a. less than h b. h c. greater than h A disk has mass M = 1.0 kg and radius, R = 0.1 m is free to rotate about a fixed axle through its center. Since the axle is fixed, the center of mass of the disk does not move. The disk is initially not rotating. A student wraps a string 12 times around the perimeter of the disk and then pulls the string with a constant force of F = 1.0 N, as shown in the figure below 16. The student pulls on the string until it is completely unwound, and the string does not slip on the disk as it is pulled. After the string has unwound, what is the angular speed of the disk : a. b. c. d. e. = 6.3 radians/sec = 17.6 radians/sec = 26.4 radians/sec = 32.8 radians/sec = 54.9 radians/sec A disk has mass M = 1.0 kg and radius, R = 0.1 m is free to rotate about a fixed axle through its center. Since the axle is fixed, the center of mass of the disk does not move. The disk is initially not rotating. A student wraps a string 12 times around the perimeter of the disk and then pulls the string with a constant force of F = 1.0 N, as shown in the figure below 17. Now suppose the student repeats the experiment, this time wrapping the string around the perimeter of the disk 6 times and pulling the string with a constant force of F = 2.0 N. As before, the disk is initially not rotating. How does the angular speed of the disk after the string unwinds, , compare to found in the previous problem? a. < b. = c. > A spool lies on a frictionless horizontal table. A string wound around the hub of the spool is pulled horizontally with a force F = 15 N. The moment of inertia of the spool about a vertical axis through its center of mass is I = 0.8 kg·m2, its outer radius is R = 0.75 m and its inner radius is r = 0.25 m. The spool starts from rest and the center of mass of the spool is observed to accelerate at a rate of 2.1 m/s2. (Note, you should not assume the moment of inertia for the spool is given by 1/2MR2) Top View M R ACM =2.1 m/s r 2 Side View F F= 15 N Frictionless Table 18. What is the mass of the disk M? a. 2.75 kg b. 5.28 kg c. 7.14 kg A spool lies on a frictionless horizontal table. A string wound around the hub of the spool is pulled horizontally with a force F = 15 N. The moment of inertia of the spool about a vertical axis through its center of mass is I = 0.8 kg·m2, its outer radius is R = 0.75 m and its inner radius is r = 0.25 m. The spool starts from rest and the center of mass of the spool is observed to accelerate at a rate of 2.1 m/s2. (Note, you should not assume the moment of inertia for the spool is given by 1/2MR2) Top View M R ACM =2.1 m/s r 2 Side View F F= 15 N Frictionless Table 19. What is the angular acceleration of the disk ? a. b. c. d. e. 2.8 rad/s2 4.7 rad/s2 8.4 rad/s2 3.3 rad/s2 7.1 rad/s2 A Physics 211 student is out shoveling snow in the driveway. At one point he holds the shovel horizontally with 5 kg of snow in the shovel’s scoop and pauses without moving it. The left hand is at the left end of the shovel, the right hand is 0.7m to the right, and the center of mass of the snow is 0.5 meters further to the right as shown in the figure below. Gravity acts in the –y direction. 20. Assuming the shovel is massless, what is the y-component Fy of the force that his left hand exerts on the shovel? a. Fy = –35 N b. Fy = –10 N c. Fy = 0 N d. Fy = 10 N e. Fy = 35 N A Physics 211 student is out shoveling snow in the driveway. At one point he holds the shovel horizontally with 5 kg of snow in the shovel’s scoop and pauses without moving it. The left hand is at the left end of the shovel, the right hand is 0.7m to the right, and the center of mass of the snow is 0.5 meters further to the right as shown in the figure below. Gravity acts in the –y direction. 21. Now suppose that the handle of the shovel has a mass of 1 kg, uniformly distributed along its 1.2 meter length. Taking into account the mass of the handle, the magnitude of the force of the student’s left hand on the end of the shovel’s handle will a. increase. b. decrease. c. stay the same. Two blocks are suspended over a pulley by a string of negligible mass as shown below. The block on the left has a mass of m1, and the block on the right has mass m2. The pulley is a uniform solid cylinder with mass M and radius R. The block on the right has a downward acceleration equal to 1/3 the acceleration due to gravity. The tension in the string supporting the mass on the left is T1 = 170N and the tension in the string supporting the mass on the right is T2 = 255N. The string does not slip on the pulley. 22. What is the mass, m2, of the block on the right? M R a. m2 = 43 kg b. m2 = 39 kg c. m2 = 26 kg T1=170N T2=255N m1 m2 23. What is the mass, M, of the pulley? a. b. c. d. e. M = 14 kg M = 27 kg M = 39 kg M = 46 kg M = 52 kg a =g/3 24. A judge’s gavel has a mass of 0.7 kg and has a moment of inertia of 0.10 kg m2 around an axis through its center of mass, perpendicular to the paper in the drawing above. The distance between the center of mass of the gavel and the end of the handle is 30 cm. What is the moment of inertia of the gavel around an axis through the end of the handle, perpendicular to the paper? a. b. c. d. e. 0.05 kg m2 0.10 kg m2 0.16 kg m2 0.20 kg m2 0.31 kg m2