Exam 12: Rotation of a Rigid Body

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.Under maximum load,find the magnitude of the x component of the force exerted on the beam by the pivot at P.

A light board,10 m long,is supported by two sawhorses,one at one edge of the board and a second at the midpoint.A small 40-N weight is placed between the two sawhorses,3.0 m from the edge and 2.0 m from the center.What forces are exerted by the sawhorses on the board?

If two forces of equal magnitude act on an object that is hinged at a pivot,the force acting farther from the pivot must produce the greater torque about the pivot.

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

A metal bar is hanging from a hook in the ceiling when it is suddenly struck by a ball that is moving horizontally (see figure).The ball is covered with glue,so it sticks to the bar.During this collision

A 120-kg refrigerator,2.00 m tall and 85.0 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 0.300.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 won't tip before it begins to slide?

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

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

In the figure,a uniform ladder 12 meters long rests against a vertical frictionless wall.The ladder weighs 400 N and makes an angle θ of 79° with the floor.A man weighing 790 N climbs slowly up the ladder When he has climbed to a point that is 7.8 m from the base of the ladder,the ladder starts to slip.What is the coefficient of static friction between the floor and the ladder?

In the figure,two blocks,of masses 2.00 kg and 3.00 kg,are connected by a light string that passes over a frictionless pulley of moment of inertia 0.00400 kg · m² and radius 5.00 cm.The coefficient of friction for the tabletop is 0.300.The blocks are released from rest.Using energy methods,find the speed of the upper block just as it has moved 0.600 m.

A very thin uniform rod,2.40 m long and of weight 135 N,has a frictionless hinge at its lower end.It starts out vertically from rest and falls,pivoting about the hinge.Just as it has rotated through an angle of 55.0°,what is the downward acceleration of the end farthest from the hinge?

A uniform sign is supported against a wall at point P as shown in the figure.If the sign is a square on a side and its mass is what is the magnitude of the horizontal force that the wall at P experiences?

An object is rotating with an angular momentum 4.00 kg ∙ m²/s while being acted on by a constant torque 3.00 N ∙ m .What is the angular speed of precession of the angular velocity of the object?

If an irregularly shaped object (such as a wrench)is dropped from rest in a classroom and feels no air resistance,it will

The two rotating systems shown in the figure differ only in that the two identical movable masses are positioned at different distances from the axis of rotation.If you release the hanging blocks simultaneously from rest,and if the ropes do not slip,which block lands first?

A uniform disk has a mass of 3.7 kg and a radius of 0.40 m.The disk is mounted on frictionless bearings and is used as a turntable.The turntable is initially rotating at 30 rpm.A thin-walled hollow cylinder has the same mass and radius as the disk.It is released from rest,just above the turntable,and on the same vertical axis.The hollow cylinder slips on the turntable for 0.20 s until it acquires the same final angular velocity as the turntable.What is the final angular momentum of the system?

A 95 N force exerted at the end of a torque wrench gives rise to a torque of 15 N ∙ m. What is the angle (assumed to be less than 90°)between the wrench handle and the direction of the applied force?

If the magnitude of the cross product of two vectors is one-half the dot product of the same vectors,what is the angle between the two vectors?

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 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?