Exam 11: Rotational Dynamics and Static Equilibrium

A 40.0-kg child running at 3.00 m/s suddenly jumps onto a stationary playground merry-go-round at a distance 1.50 m from the axis of rotation of the merry-go-round.The child is traveling tangential to the edge of the merry-go-round just before jumping on.The moment of inertia about its axis of rotation is 600 kg ∙ m² and very little friction at its rotation axis.What is the angular speed of the merry-go-round just after the child has jumped onto it?

The drive chain in a bicycle is applying a torque of 0.850 N ∙ m to the wheel of the bicycle.You can treat the wheel as a thin uniform hoop (or ring)with a mass of 0.750 kg and a radius of 33.0 cm.What is the angular acceleration of the wheel?

A 320-g ball and a 400-g ball are attached to the two ends of a string that goes over a pulley with a radius of 8.7 cm.Because of friction in its axle,the pulley does not begin to rotate.What is the magnitude of the frictional torque at the axle of the pulley if the system remains at rest when the balls are released?

A solid wood door,90.0 cm wide by 2.00 m tall has a mass of 35.0 kg.It is open and at rest.A small 500-g ball is thrown perpendicular to the door with a speed of 20.0 m/s and hits the door 60.0 cm from the hinged side.The ball rebounds with a speed of 16.0 m/s along the same line.What is the angular speed of the door just after the collision with the ball?

The lug nuts on a car wheel require tightening to a torque of 90 N ∙ m.If a 30-cm long wrench is used,what is the magnitude of the minimum force required using the wrench?

A torque of 12 N ∙ m is applied to a solid,uniform disk of radius 0.50 m.If the disk accelerates at What is the mass of the disk?

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 magnitude of the net force that the bolt exerts on the sign?

A force of Is applied tangentially to a wheel of radius 0.340 m and causes an angular acceleration of 1.20 rad/s².What is the moment of inertia of the wheel?

A mechanic is examining the wheel of a bicycle to adjust the brake.With the bicycle off the ground,he manually rotates the wheel until it reaches an angular speed of 12.0 rad/s and then allows it to coast to a stop.If the wheel has a moment of inertia of 0.100 kg ∙ m²,and the wheel slows uniformly to a stop in 160 s,what is the magnitude of the retarding torque?

A 95-N force exerted at the end of a 0.32-m long torque wrench produces a torque of 15 N ∙ m.What is the angle (less than 90°)between the wrench handle and the direction of the applied force?

A particular motor can provide a maximum torque of 110 N ∙ m.Assuming that all of this torque is used to accelerate a solid,uniform,cylindrical flywheel of mass 10.0 kg and radius 3.00 m,how long will it take for the flywheel to accelerate from rest to

A mobile is shown in the figure.The horizontal supports have negligible mass.Assume that all the numbers given in the figure are accurate to two significant figures.What mass M is required to balance the mobile?

Two equal-magnitude forces are applied to a door at the doorknob.The first force is applied perpendicular to the door,and the second force is applied at 30° to the plane of the door.Which force exerts the greater torque about the door hinge?

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

Three solid,uniform,cylindrical flywheels,each of mass 65.0 kg and radius 1.47 m,rotate independently around a common axis through their centers.Two of the flywheels rotate in one direction at 8.94 rad/s,but the other one rotates in the opposite direction at 3.42 rad/s.Calculate the magnitude of the net angular momentum of the system.

A 385-g tile hangs from one end of a string that goes over a pulley with a moment of inertia of 0.0125 kg.m². And a radius of 15.0 cm.A mass of 710 g hangs from the other end of the string.When the tiles are released,the larger one accelerates downward while the lighter one accelerates upward.The pulley has no friction in its axle and turns without the string slipping.What is the tension in the string on the side of the 710-g tile?

A uniform solid cylinder of mass 10 kg can rotate about a frictionless axle through its center O,as shown in the cross-sectional view in the figure.A rope wrapped around the outer radius R₁ = 1.0 m exerts a force of magnitude F₁ = 5.0 N to the right.A second rope wrapped around another section of radius R₂ = 0.50 m exerts a force of magnitude F₂ = 6.0 N downward.How many radians does the cylinder rotate through in the first 5.0 seconds,if it starts from rest?

If the answer to your calculation has units of kg ∙ m²/s,what type of quantity could it be? (There could be more than one correct choice).

An athlete holds a 7.5-kg shot put in his hand with his lower arm horizontal,as shown in the figure.His lower arm has a mass of 2.8 kg and its center of gravity (or center of mass)is 12 cm from the elbow-joint pivot.How much force must the extensor muscle (which is _M in the figure)in the upper arm exert on the lower arm?

The rotating systems shown in the figure differ only in that the two identical movable masses are positioned a distance r from the axis of rotation (left),or a distance r/2 from the axis of rotation (right).If you release the hanging blocks simultaneously from rest,and call t_L the time taken by the block on the left and t_R the time taken by the block on the right to reach the bottom,respectively,then