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Exam 9: Rotational Dynamics

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Question 1

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A meter stick is pivoted at the 0.50-m line.A 3.0-kg object is hung from the 0.15-m line.Where should a 5.0-kg object be hung to achieve equilibrium (the meter stick oriented horizontal and motionless) ?

A) 0.06-m line
B) 0.24-m line
C) 0.56-m line
D) 0.71-m line
E) A 5.0-kg object cannot be placed anywhere on the meter stick to result in equilibrium in this system.

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Question 2

Multiple Choice

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A spinning skater draws in her outstretched arms thereby reducing her moment of inertia by a factor of 2.Determine the ratio of her final kinetic energy to her initial kinetic energy.

A) 0.5
B) 1
C) 2
D) 4
E) 16

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Question 3

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A hollow cylinder of mass M and radius R rolls down an inclined plane.A block of mass M easily slides down an identical inclined plane.Complete the following statement: If both objects are released at the same time from the top of their inclined planes,

A child standing on the edge of a freely spinning merry-go-round moves quickly to the center.Which one of the following statements is necessarily true concerning this event and why?

A solid cylinder of radius 0.35 m is released from rest from a height of 1.8 m and rolls down the incline as shown.What is the angular speed of the cylinder when it reaches the horizontal surface?

A solid sphere rolls without slipping along a horizontal surface.What percentage of its total kinetic energy is rotational kinetic energy?

Consider the following four objects: a hoop, a flat disk, a solid sphere, and a hollow sphere.Each of the objects has mass M and radius R.The axis of rotation passes through the center of each object, and is perpendicular to the plane of the hoop and the plane of the flat disk.Which of these objects requires the largest torque to give it the same angular acceleration?

A ceiling fan has five blades, each with a mass of 0.34 kg and a length of 0.66 m.The fan is operating in its "low" setting at which the angular speed is 9.4 rad/s.If the blades can be approximated as uniform thin rods that rotate about one end, what is the total rotational kinetic energy of the five blades?

A solid sphere and a hollow sphere each of mass M and radius R are released at the same time from the top of an inclined plane.Which one of the following statements is necessarily true?

A ball of mass M moves in a circular path on a horizontal, frictionless surface.It is attached to a light string that passes through a hole in the center of the table.If the string is pulled down, thereby reducing the radius of the path of the ball, the speed of the ball is observed to increase.Complete the following sentence: This occurs because

An 80-kg man balances the boy on a teeter-totter as shown.Note: Ignore the weight of the board. -Which one of the following statements most accurately describes the center of gravity of an object?

A 1500-kg satellite orbits a planet in a circular orbit of radius 6.2 × 10⁶ m.What is the angular momentum of the satellite in its orbit around the planet if the satellite completes one orbit every 1.5 × 10⁴ s?

A steady horizontal force of magnitude 21 N is applied at the axle of a solid disk as shown.The disk has mass 2.0 kg and diameter 0.10 m.What is the linear speed of the center of the disk after it has moved 12 m?

Planets A and B are uniform solid spheres that rotate at a constant speed about axes through their centers.Although B has twice the mass and three times the radius of A, each planet has the same rotational kinetic energy.What is the ratio $\omega$ _B/ $\omega$ _A of their angular speeds?

Two skaters, each of mass 40 kg, approach each other along parallel paths that are separated by a distance of 2 m.Both skaters have a speed of 10 m/s.The first skater carries a 2-m pole that may be considered massless.As he passes the pole, the second skater catches hold of the end.The two skaters then go around in a circle about the center of the pole. -What is the angular speed of the skaters after they have linked together?

A 60.0-kg skater begins a spin with an angular speed of 6.0 rad/s.By changing the position of her arms, the skater decreases her moment of inertia to one-half its initial value.What is the skater's final angular speed?

Two equal spheres, labeled A and B in the figure, are attached to a massless rod with a frictionless pivot at the point P.The system is made to rotate clockwise with angular speed $\omega$ on a horizontal, frictionless tabletop.Sphere A collides with and sticks to another equal sphere that is at rest on the tabletop.Note: the masses of all three spheres are equal. What is the angular speed of the system immediately after the collision?

One end of a rope is tied to the handle of a horizontally-oriented and uniform door.A force is applied to the other end of the rope as shown in the drawing.The door has a weight of 145 N and is hinged on the right.What is the maximum magnitude of for which the door will remain at rest?

A 4.0-kg ball moves in a straight line at 8.0 m/s as shown in the figure.At the instant shown, what is its angular momentum about the point P?

What happens when a spinning ice skater draws in her outstretched arms?