Exam 12: Rotation of a Rigid Body

A 5.0-m radius playground merry-go-round with a moment of inertia of 2000 kg ∙ m² is rotating freely with an angular speed of 1.0 rad/s.Two people,each having a mass of 60 kg,are standing right outside the edge of the merry-go-round and step on it with negligible speed.What is the angular speed of the merry-go-round right after the two people have stepped on?

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 uniform disk,a uniform hoop,and a uniform solid sphere are released at the same time at the top of an inclined ramp.They all roll without slipping.In what order do they reach the bottom of the ramp?

A turbine blade rotates with angular velocity ω(t)= 2.00 rad/s- 2.1.00 rad/s³ .What is the angular acceleration of the blade at

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?

In the figure,a mass of 31.77 kg is attached to a light string that is wrapped around a cylindrical spool of radius 10.0 cm and moment of inertia 4.00 kg · m².The spool is suspended from the ceiling,and the mass is then released from rest a distance 5.70 m above the floor.How long does it take to reach the floor?

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).The percent of the initial kinetic energy of the system that is lost during the capture of the ball is closest to

A uniform solid sphere has a moment of inertia I about an axis tangent to its surface.What is the moment of inertia of this sphere about an axis through its center?

A child is trying to stack two uniform wooden blocks,12 cm in length,so they will protrude as much as possible over the edge of a table,without tipping over,as shown in the figure.What is the maximum possible overhang distance d?

If = -4 - 2 - 3 ,what is × ?

A uniform piece of wire,20 cm long,is bent in a right angle in the center to give it an L-shape.How far from the bend is the center of mass of the bent wire?

A uniform solid cylinder of radius R and a thin uniform spherical shell of radius R both roll without slipping.If both objects have the same mass and the same kinetic energy,what is the ratio of the linear speed of the cylinder to the linear speed of the spherical shell?

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?

A very thin horizontal,2.00-m long,5.00-kg uniform beam that lies along the east-west direction is acted on by two forces.At the east end of the beam,a 200-N force pushes downward.At the west end of the beam,a 200-N force pushes upward.What is the angular acceleration of the beam?

A futuristic design for a car is to have a large solid disk-shaped flywheel within the car storing kinetic energy.The uniform flywheel has mass 370 kg with a radius of 0.500 m and can rotate up to Assuming all of this stored kinetic energy could be transferred to the linear velocity of the car,find the maximum attainable speed of the car.

Two identical ladders are 3.0 m long and weigh 600 N each.They are connected by a hinge at the top and are held together by a horizontal rope,1.0 m above the smooth floor forming a symmetric "A" arrangement.The angle between the ladders is 60° and both ladders have their center of gravity at their midpoint.What is the tension in the rope?

For the vectors shown in the figure,find the magnitude and direction of × ,assuming that the quantities shown are accurate to two significant figures.

A 20.0-kg uniform door has a width of 1.20 m and a height of 2.50 m.The door is mounted on a post by a pair of hinges,marked 1 and 2 in the figure,at the top and bottom of the door.An external force of 60.0 N,at an angle of 30.0° above the horizontal,is applied to the small doorknob,as shown in the figure.The doorknob is 1.00 m above the bottom of the door. (a)Find the x component of the force that hinge 1 exerts on the door at the top. (b)Find the SUM of the y components of the forces that hinges 1 and 2 together exert on the door.

A uniform solid sphere is rolling without slipping along a horizontal surface with a speed of 5.50 m/s when it starts up a ramp that makes an angle of 25.0° with the horizontal.What is the speed of the sphere after it has rolled 3.00 m up the ramp,measured along the surface of the ramp?

In the figure,four point masses are placed as shown.The x and y coordinates of the center of mass are closest to