Exam 12: Rotation of a Rigid Body

A uniform solid disk of radius 1.60 m and mass 2.30 kg rolls without slipping to the bottom of an inclined plane.If the angular velocity of the disk is at the bottom,what is the height of the inclined plane?

A 4.50-kg wheel that is 34.5 cm in diameter rotates through an angle of 13.8 rad as it slows down uniformly from 22.0 rad/s to 13.5 rad/s.What is the magnitude of the angular acceleration of the wheel?

A lawn roller in the form of a uniform solid cylinder is being pulled horizontally by a horizontal force B applied to an axle through the center of the roller,as shown in the figure.The roller has radius 0.65 meters and mass 51 kg and rolls without slipping.What magnitude of the force B is required to give the center of mass of the roller an acceleration of ?

A horizontal disk rotates about a vertical axis through its center.Point P is midway between the center and the rim of the disk,and point Q is on the rim.If the disk turns with constant angular velocity,which of the following statements about it are true? (There may be more than one correct choice.)

In the figure,a 10.0-m long bar is attached by a frictionless hinge to a wall and held horizontal by a rope that makes an angle θ of 53° with the bar.The bar is uniform and weighs 39.9 N.How far from the hinge should a 10.0-kg mass be suspended for the tension T in the rope to be 125 N?

In the figure,a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface.The crate weighs 930 N,and its center of gravity is at its geometric center.A horizontal force F is applied at a distance h above the floor.If what minimum value of F is required to make the crate start to tip over? Static friction is large enough that the crate does not start to slide.

When a 2.75-kg fan,having blades 18.5 cm long,is turned off,its angular speed decreases uniformly from 10.0 rad/s to 6.30 rad/s in 5.00 s. (a)What is the magnitude of the angular acceleration of the fan? (b)Through what angle (in degrees)does it turn while it is slowing down during the 5.00 s? (c)If its angular acceleration does not change,how long after it is turned off does it take the fan to stop.

A solid uniform brick is placed on a sheet of wood.When one end of the sheet is raised (see figure),you observe that the maximum that the angle θ can be without tipping over the brick is 49.6°.There is enough friction to prevent the brick from sliding.What is the width w of the brick?

The angular velocity of a 755-g wheel 15.0 cm in diameter is given by the equation ω(t)= (2.00 rad/s²)t + (1.00 rad/s⁴)t³. (a)Through how many radians does the wheel turn during the first 2.00 s of its motion? (b)What is the angular acceleration (in rad/s²)of the wheel at the end of the first 2.00 s of its motion?

A ball is released from rest on a no-slip surface,as shown in the figure.After reaching its lowest point,the ball begins to rise again,this time on a frictionless surface as shown in the figure.When the ball reaches its maximum height on the frictionless surface,it is

A potter's wheel,with rotational inertia 46 kg ∙ m²,is spinning freely at 40 rpm.The potter drops a lump of clay onto the wheel,where it sticks a distance 1.2 m from the rotational axis.If the subsequent angular speed of the wheel and clay is 32 rpm what is the mass of the clay?

A uniform 300-kg beam,6.00 m long,is freely pivoted at P,as shown in the figure.The beam is supported in a horizontal position by a light strut,5.00 m long,which is freely pivoted at Q and is loosely pinned to the beam at R.A load of mass is suspended from the end of the beam at S.A maximum compression of 23,000 N in the strut is permitted,due to safety.The maximum mass M of the load is closest to

A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle.Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices.

At any angular speed,a certain uniform solid sphere of diameter D has half as much rotational kinetic energy as a certain uniform thin-walled hollow sphere of the same diameter when both are spinning about an axis through their centers.If the mass of the solid sphere is M,the mass of the hollow sphere is

For the apparatus shown in the figure,there is no slipping between the cord and the surface of the pulley.The blocks have mass of 3.0 kg and 5.7 kg,and the pulley has a radius of 0.12 m and a mass of 10.3 kg.At the instant the 5.7 kg mass has fallen 1.5 m starting from rest,find the speed of each block.(Assume the pulley is in the shape of a uniform solid disk and has no friction in its axle.)

A dumbbell-shaped object is composed by two equal masses,m,connected by a rod of negligible mass and length r.If I₁ is the moment of inertia of this object with respect to an axis passing through the center of the rod and perpendicular to it and I₂ is the moment of inertia with respect to an axis passing through one of the masses,it follows that

A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg · m².The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings.A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s.The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure).What is the angular velocity of the turntable just after the ball is caught?

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).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.The bar,pulley,and rope have negligible mass,the rope does not slip,and there is no friction in the axle of the pulley.Under these conditions

Consider a uniform solid sphere of radius R and mass M rolling without slipping.Which form of its kinetic energy is larger,translational or rotational?

A uniform solid sphere of mass 1.5 kg and diameter 30.0 cm starts from rest and rolls without slipping down a 35° incline that is 7.0 m long. (a)Calculate the linear speed of the center of the sphere when it reaches the bottom of the incline. (b)Determine the angular speed of the sphere about its center at the bottom of the incline. (c)Through what angle (in radians)does this sphere turn as it rolls down the incline? (d)Does the linear speed in (a)depend on the radius or mass of the sphere? Does the angular speed in (b)depend on the radius or mass of the sphere?