Exam 8: Rotational Equilibrium and Dynamics

A uniform rod of length L and mass M is pivoted about one end.Attached to the rod is a mass M at its midpoint and at the end opposite the pivot is another mass M.What is the moment of inertia of this configuration about the pivot?

A 2.00-kg mass is placed at (3.00,4.00)m,and a 3.50-kg mass is placed at (3.00,−4.00)m.What is the moment of inertia of this system of masses about the z axis?

Three disks have the same mass and the same total kinetic energy.Disk #1 has radius R,disk #2 has radius 2R,and disk #3 has radius 3R.Which one has the highest v_{translational}?

A meter stick is hinged at its lower end and allowed to fall from a vertical position.If its moment of inertia is ML²/3,with what angular speed does it hit the table?

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 bucket filled with water has a mass of 20.0 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 = 9.80 m/s²)

A solid sphere of radius R is placed on an incline that makes an angle ​θ with the horizontal.The sphere rolls down the incline without slipping.What is its acceleration?

Tasha has mass 20 kg and wants to use a 5.0-m board of mass 12 kg as a seesaw.Her friends are busy,so Tasha seesaws by herself by putting the support at the system's center of gravity when she sits on one end of the board.How far is she from the support point?

A turntable has a moment of inertia of 3.00 × 10−² kg·m² and spins freely on a frictionless bearing at 25.0 rev/min.A 0.600-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?

Two hoops or rings (I = MR²)are centered,lying on a turntable.The smaller ring has radius = 0.05 m;the larger has radius = 0.10 m.Both have a mass of 5.0 kg.What is the total moment of inertia as the turntable spins? Ignore the mass of the turntable.

A 60-kg man is one fourth of the way up a 10-m ladder that is resting against a smooth,frictionless wall.If the ladder has a mass of 25 kg and it makes an angle of 60° with the ground,find the force of friction of the ground on the foot of the ladder.

A baseball pitcher,loosening up his arm before a game,tosses a 0.140-kg ball using only the rotation of his forearm,0.290 m in length,to accelerate the ball.If the ball starts at rest and is released with a speed of 24.0 m/s in a time of 0.450 s,what is the average angular acceleration of the arm and ball?

A rod system with a uniform linear density of $\lambda$ = 4.40 kg/m has the shape shown in the figure,with rod 1 the vertical rod and rod 2 the horizontal rod.Rod 1 has length L₁ = 8.00 m,and rod 2 has length L₂ = 7.50 m.Neglect the diameter of the rods. ​ -What is the center of mass of each rod?

A figure skater with arms initially extended starts spinning on the ice at 3 rad/s.She then pulls her arms in close to her body.Which of the following results?

A figure skater on ice with arms extended,spins at a rate of 3.5 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 rod system with a uniform linear density of $\lambda$ = 4.40 kg/m has the shape shown in the figure,with rod 1 the vertical rod and rod 2 the horizontal rod.Rod 1 has length L₁ = 8.00 m,and rod 2 has length L₂ = 7.50 m.Neglect the diameter of the rods. ​ -What is the mass of each rod?

An ice skater spins at 3.5 rev/s with his arms are extended.He draws his arms in and spins at 8.3 rev/s.By what factor does his moment of inertia change in the process?

A rotating flywheel can be used as a method to store energy.If it has 2.00 × 10⁶ J of kinetic energy when rotating at 400 rad/s,and if a frictional torque of 4.00 N M acts on the system,in what interval of time would the flywheel come to rest?

A meterstick is supported by a knife-edge at the 50.0-cm mark.Doug hangs masses of 0.48 and 0.76 kg from the 10-cm and 80-cm marks,respectively.Where should Doug hang a third mass of 0.25 kg to keep the stick balanced?

A uniform bridge span weighs 70.0 kN and is 40.0 m long.An automobile weighing 15.0 kN is parked with its center of gravity located 15.0 m from the right pier.What upward support force does the right pier provide?