Exam 8: Rotational Equilibrium and Rotational Dynamics

An ice skater spins at 2.5 rev/s when his arms are extended.He draws his arms in and spins at 6.0 rev/s.By what factor does his moment of inertia change in the process?

A 40-kg boy is standing on the edge of a stationary 30-kg platform that is free to rotate.The boy tries to walk around the platform in a counterclockwise direction.As he does:

The Earth's gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit.Compare the motion of the satellite at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee).At these two points:

A turntable has a moment of inertia of 3.0 * 10^-2 kg*m² and spins freely on a frictionless bearing at 25 rev/min.A 0.30-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.10 m from the center.By what factor does the kinetic energy of the system change after the putty is dropped onto the turntable?

A meter stick is supported by a knife-edge at the 50-cm mark.Doug hangs masses of 0.40 and 0.60 kg from the 20-cm and 80-cm marks, respectively.Where should Doug hang a third mass of 0.30 kg to keep the stick balanced?

A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3 000 rpm) by an electric motor.The flywheel is a solid cylinder of mass 500 kg and radius 0.500 m (I_cylinder = MR²/2).If the bus requires an average power of 10.0 kW, how long will the flywheel rotate?

An object consists of a rod (of length 3.0 m and negligible moment of inertia) to which four small 2.0-kg masses are attached, one at each end and one at each point on the rod 1.0 m from each end.(The masses are one meter apart.) The moment of inertia of this object about an axis perpendicular to the rod and through one of the inner masses:

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m.What is the moment of inertia of this system of masses about the z-axis?

A solid disk of radius R rolls down an incline in time T.The center of the disk is removed up to a radius of R/2.The remaining portion of the disk with its center gone is again rolled down the same incline.The time it takes is:

The Earth's gravity exerts no torque on a satellite orbiting the Earth in an elliptical orbit.Compare the motion at the point nearest the Earth (perigee) to the motion at the point farthest from the Earth (apogee).At the point closest to the Earth:

The Earth moves about the Sun in an elliptical orbit.As the Earth moves closer to the Sun, which of the following best describes the Earth-Sun system's moment of inertia?

Consider the use of the terms "rotation" and "revolution".In physics:

A uniform, horizontal beam of length 6.0 m and weight 120 N is attached at one end to a wall by a pin connection (so that it may rotate).A cable attached to the wall above the pin supports the opposite end.The cable makes an angle of 60 $\degree$ with the horizontal.What is the tension in the cable needed to maintain the beam in equilibrium?

A majorette takes two batons and fastens them together in the middle at right angles to make an "x" shape.Each baton was 0.80 m long and each ball on the end is 0.20 kg.(Ignore the mass of the rods.) What is the moment of inertia if the arrangement is spun around an axis formed by one of the batons?

An object of radius R and moment of inertia I rolls down an incline of height H after starting from rest.Its total kinetic energy at the bottom of the incline:

A ventilation fan with a moment of inertia of 0.034 kg*m² has a net torque of 0.11 N*m applied to it.What angular acceleration does it experience?

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 * 10^-2 kg*m² and a radius of 0.10 m.If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its total kinetic energy?

An object of mass m and moment of inertia I has rotational kinetic energy K_R.Its angular momentum is:

A 4.0-kg mass is placed at (3.0, 4.0) m, and a 6.0-kg mass is placed at (3.0, -4.0) m.What is the moment of inertia of this system of masses about the y-axis?

A bucket filled with water has a mass of 23 kg and is attached to a rope, which in turn, is wound around a 0.050-m radius cylinder at the top of a well.What torque does the weight of water and bucket produce on the cylinder if the cylinder is not permitted to rotate? (g = 9.8 m/s²)