Exam 9: Rotational Dynamics

A wrench is used to tighten a nut as shown in the figure. A 12-N force is applied 7.0 cm from the axis of rotation. What is the magnitude of the torque due to the applied force?

A certain merry-go-round is accelerated uniformly from rest and attains an angular speed of 1.2 rad/s in the first 18 seconds. If the net applied torque is 1200 N . m, what is the moment of inertia of the merry-go-round?

A 1.0-kg wheel in the form of a solid disk rolls along a horizontal surface with a speed of 6.0 m/s. What is the total kinetic energy of the wheel?

Three children are pulling on a rotatable platform on a playground. The platform has a radius of 3.80 m. In the picture, two children are pulling with equal forces of 40.0 N in an attempt to make the platform rotate clockwise. The third child applies a force of 60 N as shown. What is the net torque on the platform? Note: "ccw" is counterclockwise and "cw" is clockwise.

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 their combined angular momentum about the center of the pole?

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?

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

A 2.0-kg hoop rolls without slipping on a horizontal surface so that its center proceeds to the right with a constant linear speed of 6.0 m/s. -What is the total kinetic energy of the hoop?

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?

In the drawing shown, the large wheel has a radius of 7.1 m. A rope is wrapped around the edge of the wheel and a 7.6 kg-box hangs from the rope. A smaller disk of radius 1.38 m is attached to the wheel. A rope is wrapped around the edge of the disk as shown. An axis of rotation passes through the center of the wheel-disk system. What is the value of the mass M that will prevent the wheel from rotating?

A uniform disk of radius 1.2 m and mass 0.60 kg is rotating at 25 rad/s around an axis that passes through its center and is perpendicular to the disk. A rod makes contact with the rotating disk with a force of 4.5 N at a point 0.75 m from the axis of rotation as shown. The disk is brought to a stop in 5.0 s. What is the coefficient of kinetic friction for the two materials in contact?

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?

An 80-kg man balances the boy on a teeter-totter as shown. Note: Ignore the weight of the board. -What, approximately, is the magnitude of the downward force exerted on the fulcrum?

A spinning star begins to collapse under its own gravitational pull. Which one of the following occurs as the star becomes smaller?

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?

Complete the following statement: A body is in translational equilibrium

Consider four point masses located as shown in the sketch. The acceleration due to gravity is the same everywhere. What is the x coordinate of the center of gravity for this system?