1) in Class Examples from the Power Points (Posted on My Wiki)

CM and Torque Review: WARNING this is not a comprehensive review of all topics covered. In addition to this packet you should also look at.

1) In class examples from the power points (posted on my wiki)

2) Class handouts (multiple choice questions, Free Response questions, and short answer)

3) Textbook problems and chapter readings: Circular Motion: 6-5 Torque: 11-1, 11-3

1) A 12-meter uniform plank of mass 80kg kilograms rests on the top of a building with 4.0 meters extended over the edge as shown above. How far can a 50-kilogram person venture past the edge of the building on the plank before the plank just begins to tip?

2) A ball attached to a string is whirled around in a horizontal circle having a radius r. If the radius of the circle is changed to 4r and the same centripetal force is applied by the string, the new speed of the ball will be______times the original value

3) A racing car is moving around the circular track of radius 400 meters shown to the right. At the instant when the car's velocity is directed due east, its acceleration is directed due south and has a magnitude of 6 meters per second squared. When viewed from above, what is the cars velocity and direction (cw or ccw)

4) To weigh a fish, a person hangs a tackle box of mass 4.5 kilograms and a cooler of mass 6 kilograms from the ends of a uniform rigid pole that is suspended by a rope attached to its center. The system balances when the fish hangs at a point 1/4 of the rod's length from the tackle box. What is the mass of the fish?

5) An object weighing 4 newtons swings on the end of a string as a simple pendulum. At the bottom of the swing, the tension in the string is 6 newtons. In terms of g, what is the magnitude of the centripetal acceleration of the object at the bottom of the swing?

6) Two objects, of masses 6 and 8 kilograms, are hung from the ends of a stick that is 70 centimeters long and has marks every l0 centimeters, as shown to the right. If the mass of the stick is negligible, at which of the points indicated should a cord be attached if the stick is to remain horizontal when suspended from the cord?

7) A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in a vertical plane. Three small objects having masses m, M, and 4M, respectively, are mounted on the rim of the wheel, as shown above. If the system is in static equilibrium, what is the value of m in terms of M?

2. (10 points)

A coin C of mass 0.0050 kg is placed on a horizontal disk at a distance of 0.14 m from the center, as shown above. The disk rotates at a constant rate in a counterclockwise direction as seen from above. The coin does not slip, and the time it takes for the coin to make a complete revolution is 1.5 s.

(a)  The figure below shows the disk and coin as viewed from above. Draw and label vectors on the figure below to show the instantaneous acceleration and linear velocity vectors for the coin when it is at the position shown.

(b)  Determine the linear speed of the coin.

(c)  The rate of rotation of the disk is gradually increased. The coefficient of static friction between the coin and the disk is 0.50. Determine the linear speed of the coin when it just begins to slip.

(d)  If the experiment in part (c) were repeated with a second, identical coin glued to the top of the first coin, how would this affect the answer to part (c) ? Explain your reasoning.

3. An object of mass M on a string is whirled with increasing speed in a horizontal circle, as shown above. When the string breaks, the object has speed Vu and the circular path has radius R and is a height h above the ground. Neglect the friction.

(a)  Determine the following, expressing all answers in terms of h, Vu and g.

i.  The time required for the object to h it the ground after the string breaks.

ii.  The horizontal distance the object travels from the time the string breaks until it hits the ground.

iii.  The speed of the object just before it hits the ground (use energy)

(b)  On the figure below, draw and label all the forces acting on the object when it

is in the position shown in the diagram above.

(c)  Determine the tension in the string just before the string breaks. Express

your answer in terms of M, R, Vu and g.