The following relates to the next two problems.

A uniform rod of mass M is supported by a string as shown. The rod is free to rotate about the end bolt opposite the string. A rod, when rotated around its center, has an inertia of (1/12)ML2.

  1. What is the tension string?
  2. .5Mg
  3. Mg
  4. 2Mg
  5. 4Mg
  6. 5Mg
  1. What is the linear acceleration at the end of the rod (string end) when the string is cut?
  2. .5g
  3. (2/3)g
  4. g
  5. (4/3)g
  6. (3/2)g
  1. Two rings of radius 2R and R are laid on top of one another, as shown. What is the distance of the center of mass from the center of the 2R ring? Assume each ring is cut from the same line of wire.
  2. (1/4)R
  3. (1/2)R
  4. (1/3)R
  5. (2/3)R
  6. (3/2)R

  1. A super bouncy ball is dropped from some height and then rebounds to its original height. Assume acceleration due to gravity is a positive vector. Which would be a plot of the net force on the ball as a function of time, from the time released until the instant it reaches the original height?
  1. For the system shown, the system is free to rotate about the center of the spool with no frictional torque. The system is released from rest. At this moment, which force statements will be true.
  2. 2*T(M)<2Mg<T(2M)
  3. 2*T(M)<2Mg=T(2M)
  4. 2*T(M) =2Mg =T(2M)
  5. 2*T(M) =2Mg>T(2M)
  6. 2*T(M)>2Mg>T(2M)
  1. A bike tire (we will assume all the mass of the tire is at the edge) has a mass M. A rope is attached to the tire spoke at a distance r from center. The angle between a radial length and the force is 60o. The radius of the tire is R. Based on the given information and the drawing, what is the initial angular acceleration of the system?
  2. (Frsin60)/(MR2)
  3. (Frcos60)/(MR2)
  4. (Fsin60)/(MR)
  5. (Fcos60)/(MR)
  6. (Frsin60)/R
  1. Solid objects that include a ring, sphere and cylinder are allowed to roll from rest down a ramp, without slipping. Which of the following is true?
  2. The ring will win
  3. The sphere will win
  4. The cylinder will win
  5. It will depend on the radius of the objects
  6. It will depend on the mass of the objects
  1. Two particles, of mass 4m and 2m are on opposite ends of a very light rod. When the rod is thrown into the air (rotating), what will be the ratio speed of 2m:4m, when the center of mass reaches maximum height?
  2. 2:1
  3. 1:1
  4. 1:1.5
  5. 1:2
  6. 1:3
  1. A uniform board, 12m long and 20Kg mass, is placed on a platform as shown below. How far can a 60Kg person walk down the board from the edge of the platform without the board being tipped over? (drawing not to scale)
  2. 2m
  3. 1.67m
  4. 1.33m
  5. .75m
  6. .6m
  1. A ball of mass 2m impacts a system fixed, as shown (completely inelastic). The system is fixed but free to rotate, as indicated Other than the impact of 2m, there are no external forces. If the 2m ball is moving at 12m/s before impact, what is the angular velocity of the system after impact, in radians/s?
  1. 2
  2. 3
  3. 6
  4. 8
  5. 12

  1. A mass is connected to a spool and released. The spool is held in place by the platform above but is free to rotate about its center. The distance the mass falls is plotted as a function of time and then graphed, as shown. The mass, m=.5Kg and r=.25m.
  2. On the spool (left) draw and identify all of the forces acting on the spool of appropriate magnitude and direction (after mass m is released).
  3. Manipulating the raw data, create a linear plot. Place the variables you intend to plot in the box provided and create the plot on the graph provided. Include appropriate quantities with their units on your graph.
  4. Determine the acceleration of the system from the plot you have created.
  5. Determine the tension on the line.
  6. Determine the inertia of the spool.
  7. Determine the force that the support system must exert upward on the spool as the mass falls. Assume the spool has a mass of 1.0Kg.