Exam 8: Rotational Equilibrium and Rotational Dynamics

A uniform solid sphere rolls down an incline of height 3 m after starting from rest.In order to calculate its speed at the bottom of the incline,one needs to know:

A rod of length L is hinged at one end.The moment of inertia as the rod rotates around that hinge is ML²/3.Suppose a 2.00-m rod with a mass of 3.00 kg is hinged at one end and is held in a horizontal position.The rod is released as the free end is allowed to fall.What is the angular acceleration as it is released?

A woman who weighs 500 N stands on an 8.0-m-long board that weighs 100 N.The board is supported at each end.The support force at the right end is 3 times the support force at the left end.How far from the right end is the woman standing?

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

An automobile accelerates from zero to 30 m/s in 6.0 s.The wheels have a diameter of 0.40 m.What is the average angular acceleration of each wheel?

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.If it starts from rest,what angular momentum will it have 8.0 s later?

A box slides down a frictionless incline,and a hoop rolls down another incline.Both inclines have the same height,and both the box and the hoop have the same mass.If both objects start from rest,upon reaching the bottom of the incline which one will have the greater kinetic energy and which one will have the greater speed?

A 4.2-kg mass is placed at (3.0,4.0)m.Where can an 8.4-kg mass be placed so that the moment of inertia about the z-axis is zero?

A bucket of water with total mass 23 kg is attached to a rope,which in turn is wound around a 0.050-m radius cylinder at the top of a well.The bucket is raised to the top of the well and released.The bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well.What is the angular speed of the cylinder at this instant?

An 800-N billboard worker stands on a 4.0-m scaffold supported by vertical ropes at each end.If the scaffold weighs 500 N and the worker stands 1.0 m from one end,what is the tension in the rope nearest the worker?

Masses are distributed in the x,y-plane as follows: 6.0 kg at (0.0,0.0)m,4.0 kg at (2.0,0.0)m,and 5.0 kg at (2.0,3.0)m.What is the x-coordinate of the center of gravity of this system of masses?

A solid sphere with mass,M,and radius,R,rolls along a level surface without slipping with a linear speed,v.What is the ratio of rotational to linear kinetic energy? (For a solid sphere,I = 0.4 MR²)

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 onto the turntable and sticks at a point 0.100 m from the center.What is the new rate of rotation of the system?

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 uniform beam of length 4.0 m and weight 100 N is mounted on an axle at one end perpendicular to the length of the beam.A rope is attached to the end of the beam at the other end from the axle and the beam is lifted by the rope so that the beam makes an angle of 30 $\degree$ with the horizontal.What is the tension in the rope if it is straight up?

A solid cylinder (I = MR²/2)has a string wrapped around it many times.When I release the cylinder,holding on to the string,the cylinder falls and spins as the string unwinds.What is the downward acceleration of the cylinder as it falls?

A tetherball is attached to a pole with a 2.0-m rope.It is circling at 0.20 rev/s.As the rope wraps around the pole it shortens.How long is the rope when the ball is moving at 5.0 m/s?

A figure skater on ice with arms extended,spins at a rate of 2.5 rev/s.After he draws his arms in,he spins at 6.0 rev/s.By what factor does the skater's kinetic energy change when he draws his arms in?

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?

A disk has a moment of inertia of 3.0 ´ 10^-4 kg*m² and rotates with an angular speed of 3.5 rad/sec.What net torque must be applied to bring it to rest within 3 s?