Exam 11: Rotational Dynamics and Static Equilibrium

A child is trying to stack two uniform bricks,each 24 cm long,so they will protrude as far as possible over the edge of a table without tipping over,as shown in the figure.What is the maximum possible overhang distance d?

Five forces act on a rod that is free to pivot at point P,as shown in the figure.Which of these forces is producing a counter-clockwise torque about point P? (There could be more than one correct choice. )

A person sits on a freely spinning lab stool that has no friction in its axle.When this person extends her arms,

A uniform 1200-N piece of medical apparatus that is 3.5 m long is suspended horizontally by two vertical wires at its ends.A small but dense 550-N weight is placed on the apparatus 2.0 m from one end,as shown in the figure.What are the tensions,A and B,in the two wires?

A 15-kg child is sitting on a playground teeter-totter,1.5 m from the pivot.What is the magnitude of the minimum force,applied 0.30 m on the other side of the pivot,that is needed to make the child lift off the ground?

A puck moves on a horizontal air table.It is attached to a string that passes through a hole in the center of the table.As the puck rotates about the hole,the string is pulled downward very slowly and shortens the radius of rotation,so the puck gradually spirals in towards the center.By what factor will the puck's angular speed have changed when the string's length has decreased to one-half of its original length?

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

Initially,a small 2.0-kg rock is whirling at the end of a very thin string in a circular path of radius 0.75 m on a horizontal frictionless surface,as shown in the figure.The initial tangential speed of the rock was 5.0 m/s.The string has been slowly winding around a vertical rod,and a few seconds later the length of the string has shortened to 0.25 m.What is the instantaneous speed of the mass at the moment the string reaches a length of 0.25 m?

A 120-kg refrigerator that is 2.0 m tall and 85 cm wide has its center of mass at its geometrical center.You are attempting to slide it along the floor by pushing horizontally on the side of the refrigerator.The coefficient of static friction between the floor and the refrigerator is 0.30.Depending on where you push,the refrigerator may start to tip over before it starts to slide along the floor.What is the highest distance above the floor that you can push the refrigerator so that it will not tip before it begins to slide?

A merry-go-round spins freely when Diego moves quickly to the center along a radius of the merry-go-round.As he does this,it is true to say that

A force of 17 N is applied to the end of a 0.63-m long torque wrench at an angle 45° from a line joining the pivot point to the handle.What is the magnitude of the torque about the pivot point produced by this force?

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.What is the angular acceleration of the cylinder?

When a car is weighed,it is driven slowly on a horizontal floor over a scale that records a reading as the front wheels go over the scale,and then records a second reading as the rear wheels go over the scale.The weight of the car is equal to

A uniform 40-N board supports two children weighing 500 N and 350 N.If the support is at the center of the board and the 500-N child is 1.5 m from its center,how far is the 350-N child from the center?

The figure shows a person's foot.In that figure,the Achilles tendon exerts a force of magnitude F = 720 N.What is the magnitude of the torque that this force produces about the ankle joint?

A 15-kg child is sitting on a playground teeter-totter,1.5 m from the pivot.What is the minimum distance,on the other side of the pivot,such that a 220-N force will make the child lift off the ground?

A uniform 135-g meter stick rotates about an axis perpendicular to the stick passing through its center with an angular speed of 3.50 rad/s.What is the magnitude of the angular momentum of the stick?

A meter stick balances at the 50.0-cm mark.If a mass of 50.0 g is placed at the 90.0-cm mark,the stick balances at the 61.3-cm mark.What is the mass of the meter stick?

A cinder block of mass m = 4.0 kg is hung from a nylon string that is wrapped around a frictionless pulley having the shape of a cylindrical shell,as shown in the figure.If the cinder block accelerates downward at 4.90 m/s² when it is released,what is the mass M of the pulley?

An ice skater has a moment of inertia of 5.0 kg ∙ m² when her arms are outstretched,and at this time she is spinning at 3.0 rev/s.If she pulls in her arms and decreases her moment of inertia to 2.0 kg ∙ m²,how fast will she be spinning?