Exam 8: Rotational Equilibrium and Rotational Dynamics

A gyroscope has a moment of inertia of 0.14 kg*m² and an initial angular speed of 15 rad/s.Friction in the bearings causes its speed to reduce to zero in 30 s.What is the value of the average frictional torque?

A turntable has a moment of inertia of 3.00 x 10^-2 kg*m² and spins freely on a frictionless bearing at 25.0 rev/min.A 0.300-kg ball of putty is dropped vertically on the turntable and sticks at a point 0.100 m from the center.By what factor does the angular momentum of the system change after the putty is dropped onto the turntable?

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 through the center perpendicular to both rods?

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:

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?

The quantity "moment of inertia" (in terms of the fundamental quantities of mass,length,and time)is equivalent to: