Exam 10: Rotation

Two children weighing 60.0 kg and 45.0 kg,respectively,are sitting at different points on the edge of a rotating merry-go-round which has a radius of 4.0 m.What is the rotational inertia for the children?

An 18-wheeler travels down the highway with a speed of 50 km/hr.Each wheel has a 30 cm radius and a mass of 16 kg.What is the total kinetic energy (translational and rotational)of all 18 wheels? (The moment of inertia of a wheel is .)

A massless string is wrapped around a cylinder of mass 0.400 kg and radius 0.100 m.The string is attached to the ceiling.The cylinder is released.As it falls,the string unwinds.What is the magnitude of the acceleration of the cylinder as it falls in m/s²?

A flywheel has mass 150 kg and radius 1.2 m,and is accelerated uniformly from rest to an angular speed of 125 radians per second in 12 seconds.What torque is required in order to accomplish this?

A spherical ball of material is rotating about its center at 35 rad/s.It has a mass of 2.0 kg and a radius of 0.11 m.If it suddenly expands to become a disk of 0.22-m radius,what will be its rate of rotation?

The mass of a star is 4.05 * 10³¹ kg and it performs one rotation in 15.00 days.Find its new period (in days)if the diameter suddenly expands to 1.450 times its original size.Assume a uniform spherical mass before the collapse and a uniform spherical mass distribution after the expansion.

The tangential force F shown in figure below is applied to a 2-kg disc with a 30-cm diameter which is allowed to rotate about an axis through its center.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,determine the disc's angular velocity after one full rotation

In opening a door,a person pushes at a point on the door 65 cm away from the hinges with a force of 50 N that is directed at an angle of 75 ^$\circ$ with respect to the surface of the door.The torque on the door about its hinges is

A meter stick and a two-meter stick have the same thicknesses and density.They are both placed upright and balancing on one end.They are then disturbed slightly from this unstable equilibrium and fall to the floor.Which one hits the ground first?

A solid cylinder of mass 1 kg and radius 5 cm is rolling without slipping on a horizontal surface.Its linear velocity is 0.2 m/s.What is its total kinetic energy?

A torque of 2.2 * 10³ Nm on a flywheel causes it to accelerate uniformly from rest to an angular speed of 125 radians per second in 12 seconds.What is the moment of inertia of the flywheel?

A force (in N)of is applied to an object at a location (in m)of (the origin is the pivot point).Find the magnitude of the torque produced {assume that each number has three significant digits}.

A massless string is wrapped around a cylinder of radius 0.100 m.A force of 100 N acts on the string.If it takes 1.2 seconds to reach an angular speed of 100 radians/s starting from rest,what is the moment of inertia of the cylinder?

A massless string is wrapped around a cylinder of mass 6.00 kg and radius 0.100 m.A force acts on the string,as shown in the diagram.If it takes 0.40 seconds to reach an angular speed of 100 radians/s starting from rest,what is the magnitude of the force,F?

A massless string is wrapped around a cylinder of radius 0.100 m.A force of 100 N acts on the string.If it takes 1.5 seconds to reach an angular speed of 100 radians/s starting from rest,what is the mass of the cylinder?

A bug (2 grams)crawls from the edge to the center of a disk that is freely turning at 20 rpm.The disk has a mass of 11 grams and a radius of 26 cm.What is the disk's new angular speed?

A person on a rotating stool with arms stretched out rotates at an angular speed of 5.00 rad/s.On bringing in his arms,the angular speed increases to 7.50 rad/s.By what factor does the moment of inertia change?

The mass of a star is 4.05 * 10³¹ kg and it performs one rotation in 15.00 days.Find its new period (in days)if the diameter suddenly shrinks to 0.450 times its original size.Assume a uniform spherical mass before the collapse and a uniform spherical mass distribution after the collapse.

The tangential force F shown in figure below is applied to a disc is allowed to rotate about an axis through its center.The diameter of the disc is 24.0 cm.The magnitude of this tangential force is given in the graph of F vs.Angular Position.With the disc at rest initially and ignoring frictional torque,the disc's angular velocity after one full rotation is -31.4 rad/sec.What is the mass of the disk?

A solid cylinder of mass m,radius r,and length L starts from rest and rolls without slipping down an inclined plane.Its vertical position decreases by a distance h.What is the final linear speed of its center of mass?