Exam 11: Rotational Dynamics and Static Equilibrium

As shown in the figure,a 35.30-kg box is attached to a light string that is wrapped around a cylindrical frictionless spool of radius 10.0 cm and moment of inertia 4.00 kg ∙ m².The spool is suspended from the ceiling,and the box is then released from rest a distance 3.50 m above the floor.How long does it take for the box to reach the floor?

A 100-kg nonuniform boom that is 6.0 m long is loosely pinned at the pivot at P.A 600-kg concrete block is suspended from the end of the boom at A,as shown in the figure.The boom forms a 30° angle above the horizontal,and is supported by a 4.0-m cable between points D and B.Point B is 4.0 m from P,and point D is 4.0 m above P.The center of mass of the boom is at point C,which is 2.0 m from P.Assume that all the quantities shown in the figure are accurate to two significant figures.What is the tension in the cable connected between points B and D?

A croquet mallet balances when suspended from its center of mass,as shown in the left part of the figure.If you cut the mallet into two pieces at its center of mass,as shown in the right part of the figure,how do the masses of the two pieces compare? (There could be more than one correct choice. )

A store's sign has a mass of 20 kg and is 3.0 m long.It is uniform,so its center of gravity is at the center of the sign.It is supported horizontally by a small loose bolt attached to the wall at one end and by a wire at the other end,as shown in the figure.What is the tension in the wire?

The drum shown in the figure has a radius of 0.40 m and a moment of inertia of 2.3 About an axis perpendicular to it through its center.The frictional torque at the drum axle is 3.0 N ∙ m.A 14-m length of rope is wound around the rim.The drum is initially at rest.A constant force is applied to the free end of the rope until the rope is completely unwound and slips off.At that instant,the angular speed of the drum is The drum then slows down at a constant rate and comes to a halt.In this situation,what was the magnitude of the constant force applied to the rope?

A 5.00-m-long uniform ladder,weighing 200 N,rests against a smooth vertical wall with its base on a horizontal rough floor,a distance of 1.20 m away from the wall.The coefficient of static friction between the ladder and the floor is 0.200.How far up the ladder,measured along the ladder,can a 600-N person climb before the ladder begins to slip?

If an object remains at rest,then the sum of both the external torques and the external forces on the object must be zero.

A 40-kg uniform ladder that is 5.0 m long is placed against a smooth wall at a height of h = 4.0 m,as shown in the figure.The base of the ladder rests on a rough horizontal surface whose coefficient of static friction with the ladder is 0.40.An 80-kg bucket is suspended from the top rung of the ladder,just at the wall.What is the magnitude of the force that the ladder exerts on the wall?

If the sum of the external forces on an object is zero,then the sum of the external torques on it must also be zero.

A stepladder consists of two halves that are hinged at the top and connected by a tie rod which keeps the two halves from spreading apart.In this particular instance,the two halves are 2.5 m long,the tie rod is connected to the center of each half and is 70 cm long.An 800-N person stands 3/5 of the way up the stepladder,as shown in the figure.The ladder is light enough that we can neglect its weight,and it rests on an extremely smooth floor.What is the tension in the tie rod? (Note: To solve this problem,it is helpful to imagine cutting the ladder in half vertically and consider the forces and torques acting on each half of the ladder. )

To determine the location of the center of mass (or center of gravity)of a car,the car is driven over a scale on a horizontal floor.When the front wheels are over the scale,the weight recorded by the scale is 5800 N,and when the rear wheels are over the scale,the scale reads 6500 N.The distance between the front and rear wheels is measured to be 3.20 m.How far behind the front wheels is the center of mass located?

Two forces produce equal torques on a door about the door hinge.The first force is applied at the midpoint of the door;the second force is applied at the doorknob.Both forces are applied perpendicular to the door.Which force has a greater magnitude?

A uniform,solid,cylindrical flywheel of radius 1.4 m and mass 15 kg rotates at What is the magnitude of the flywheel's angular momentum?

A man in a gym is holding an 8.0-kg weight at arm's length,a distance of 0.55 m from his shoulder joint.What is the torque about his shoulder joint due to the weight if his arm is horizontal?

A 3.00-m-long ladder,weighing 200 N,leans against a smooth vertical wall with its base on a horizontal rough floor,a distance of 1.00 m away from the wall.The ladder is not completely uniform,so its center of gravity is 1.20 m from its base.What force of friction must the floor exert on the base of the ladder to prevent the ladder from sliding down?

A solid wooden door,90 cm wide by 2.0 m tall,has a mass of 35 kg.It is open and at rest.A small 500-g ball is thrown perpendicular to the door with a speed of 20 m/s and hits the door 60 cm from the hinged side,causing it to begin turning.The ball rebounds along the same line with a speed of 16.0 m/s relative to the ground.How much energy is lost during this collision?

As shown in the figure,a given force is applied to a rod in several different ways.In which case is the torque about the pivot P due to this force the greatest?

In the figure,a uniform ladder of weight 200 N and length 10 m leans against a perfectly smooth wall.A firefighter of weight 600 N climbs a distance x up the ladder.The coefficient of static friction between the ladder and the floor is 0.50.What is the maximum value of x for which the ladder will not slip?

In a laboratory experiment,a student brings up the rotational speed of a flywheel to 30.0 rpm.She then allows it to slow down on its own,and counts 240 revolutions before the apparatus uniformly comes to a stop.The moment of inertia of the flywheel is 0.0850 kg ∙ m².What is the magnitude of the retarding torque on the flywheel?

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg ∙ m².If he pulls in his arms so his moment of inertia decreases to 1.80 kg ∙ m²,what will be his new angular speed?