Exam 12: Rotation of a Rigid Body

A solid uniform sphere of mass 1.85 kg and diameter 45.0 cm spins about an axle through its center. Starting with an angular velocity of 2.40 rev/s, it stops after turning through 18.2 rev with uniform acceleration. The net torque acting on this sphere as it is slowing down is closest to

A record is dropped vertically onto a freely rotating (undriven) turntable. Frictional forces act to bring the record and turntable to a common angular speed. If the rotational inertia of the record is 0.54 times that of the turntable, what percentage of the initial kinetic energy is lost?

A dump truck has a large cubical concrete block in its bed. The coefficients of friction between this block and the floor of the bed are µ_k = 0.450 and µ_s = 0.650. As the bed is slowly tilted above the horizontal, will the brick first begin to slide or will it first tip over?

A 95 N force exerted at the end of a 0.50 m long torque wrench gives rise to a torque of What is the angle (assumed to be less than 90°) between the wrench handle and the direction of the applied force?

As you are leaving a building, the door opens outward. If the hinges on the door are on your right, what is the direction of the angular velocity of the door as you open it?

A 3.00-kg ball rests in a frictionless groove as shown in the figure. (a) What is the magnitude of the force that the left side of the groove exerts on the ball? (b) What is the magnitude of the force that the right side of the groove exerts on the ball?

If = -2 - 6 + 2 And = -2 -2 - 3 , which of the following numbers is closest to the magnitude of × ?

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?

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

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?

A 500-g particle is located at the point = 4m + 3m - 2m And is moving with a velocity = 5 m/s -2 ms + 4 m/s . What is the angular momentum of this particle about the origin?

A torque of 12 N ∙ m is applied to a solid, uniform disk of radius 0.50 m, causing the disk to accelerate at 5.7 rad/s². What is the mass of the disk?

In the figure, a very light rope is wrapped around a wheel of radius R = 2.0 meters and does not slip. The wheel is mounted with frictionless bearings on an axle through its center. A block of mass 14 kg is suspended from the end of the rope. When the system is released from rest it is observed that the block descends 10 meters in 2.0 seconds. What is the moment of inertia of the wheel?