Exam 12: Rotation of a Rigid Body

A 10.0-kg uniform ladder that is 2.50 m long is placed against a smooth vertical wall and reaches to a height of 2.10 m,as shown in the figure.The base of the ladder rests on a rough horizontal floor whose coefficient of static friction with the ladder is 0.800.An 80.0-kg bucket of concrete is suspended from the top rung of the ladder,right next to the wall,as shown in the figure.What is the magnitude of the friction force that the floor exerts on the ladder?

A uniform hollow spherical ball of mass 1.75 kg and radius 40.0 cm rolls without slipping up a ramp that rises at 30.0° above the horizontal.The speed of the ball at the base of the ramp is 2.63 m/s.While the ball is moving up the ramp,find (a)the acceleration (magnitude and direction)of its center of mass and (b)the friction force (magnitude and direction)acting on it due to the surface of the ramp.

In the figure,point P is at rest when it is on the x-axis.The linear speed of point P when it reaches the y-axis is closest to

A 3.45-kg centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration.A point located 8.00 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full speed. (a)What is the angular acceleration (in rad/s²)of the centrifuge as it spins up? (b)How many revolutions does the centrifuge make as it goes from rest to its final angular speed?

In the figure,the horizontal lower arm has a mass of 2.8 kg and its center of gravity is 12 cm from the elbow joint pivot.How much force F_M must the vertical extensor muscle in the upper arm exert on the lower arm to hold a 7.5 kg shot put?

A uniform solid sphere of mass M and radius R rotates with an angular speed ω about an axis through its center.A uniform solid cylinder of mass M,radius R,and length 2R rotates through an axis running through the central axis of the cylinder.What must be the angular speed of the cylinder so it will have the same rotational kinetic energy as the sphere?

If the torque on an object adds up to zero

When you ride a bicycle,in what direction is the angular velocity of the wheels?

In the figure,a 60-cm length of uniform wire,of 60 g mass and negligible thickness,is bent into a right triangle.The x and y coordinates of the center of mass,in cm,are closest to

If two vectors point in opposite directions,their cross product must be zero.

While spinning down from 500.0 rpm to rest,a solid uniform flywheel does of work.If the radius of the disk is what is its mass?

An extremely light rod 1.00 m long has a 2.00-kg mass attached to one end and a 3.00-kg mass attached to the other.The system rotates at a constant angular speed about a fixed axis perpendicular to the rod that passes through the rod 30.0 cm from the end with the 3.00-kg mass attached.The kinetic energy of the system is measured to be 100.0 J. (a)What is the moment of inertia of this system about the fixed axis? (b)What is the angular speed (in revolutions per second)of this system?

A 20.0-kg uniform plank is supported by the floor at one end and by a vertical rope at the other as shown in the figure.A 50.0-kg mass person stands on the plank a distance three-fourths of the length plank from the end on the floor. (a)What is the tension in the rope? (b)What is the magnitude of the force that the floor exerts on the plank?

In the figure,a weightlifter's barbell consists of two identical uniform spherical masses each with radius 0.17 m and mass of 50 kg.The weights are connected by a 0.96-m uniform steel rod with a mass of 12 kg.Find the moment of inertia of the barbell about the axis through the center (see figure).

A heavy boy and a lightweight girl are balanced on a massless seesaw.If they both move forward so that they are one-half their original distance from the pivot point,what will happen to the seesaw? Assume that both people are small enough compared to the length of the seesaw to be thought of as point masses.

A solid,uniform sphere of mass 2.0 kg and radius 1.7 m rolls from rest without slipping down an inclined plane of height 7.0 m.What is the angular velocity of the sphere at the bottom of the inclined plane?

A wheel has a radius of 0.40 m and is mounted on frictionless bearings.A block is suspended from a rope that is wound on the wheel and attached to it (see figure).The wheel is released from rest and the block descends 1.5 m in 2.00 s without any slipping of the rope.The tension in the rope during the descent of the block is 20 N.What is the moment of inertia of the wheel?

Three solid,uniform,cylindrical flywheels,each of mass 65.0 kg and radius 1.47 m rotate independently around a common axis.Two of the flywheels rotate in one direction at the other rotates in the opposite direction at 3.42 rad/s.Calculate the magnitude of the net angular momentum of the system.

A nonuniform,80.0-g,meterstick balances when the support is placed at the 51.0-cm mark.At what location on the meterstick should a 5.00-g tack be placed so that the stick will balance at the 50.0 cm mark?

A 30.0-kg child sits on one end of a long uniform beam having a mass of 20.0 kg,and a 40.0-kg child sits on the other end.The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child.How long is the beam?