Exam 11: Motion in a Circle

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 230 rev/s.Assuming all of this stored kinetic energy could be transferred to the linear velocity of the 1600-kg car,find the maximum attainable speed of the car.

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?

A machinist turns the power on to a grinding wheel,which is at rest at time t = 0.00 s.The wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 25 rad/s. The wheel is run at that angular velocity for 37 s and then power is shut off.The wheel decelerates uniformly at 1.5 rad/s² until the wheel stops.In this situation,the time interval of angular deceleration (slowing down)is closest to:

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?

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?

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 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?

In the figure,point P is at rest when it is on the x-axis.The time t,when P returns to the original position on the x-axis,is closest to

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

An electrical motor spins at a constant 2857.0 rev/min. If the armature radius is 2.685 cm,what is the acceleration of the outer edge of the armature?

Two forces act on a 55-kg object.One force has magnitude 65 N directed 59° clockwise from the positive x-axis,and the other has a magnitude 35 N at 32° clockwise from the positive y-axis.What is the magnitude of this object's acceleration?

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.

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 3.83 rad/s; the other rotates in the opposite direction at 3.42 rad/s.Calculate the magnitude of the net angular momentum of the system.

A turbine blade rotates with angular velocity ω(t)= 2.00 rad/s- 2.1.00 rad/s³ t².What is the angular acceleration of the blade at t = 9.10 s?

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?

If you swing a bucket of water fast enough in a vertical circle,at the highest point the water does not spill out because an outward force balances the pull of gravity on the water.

A satellite orbits the earth a distance of 1.50 × 10⁷ m above the planet's surface and takes 8.65 hours for each revolution about the earth.The earth's radius is 6.38 × 10⁶ m.The acceleration of this satellite is closest to

Point P in the figure indicates the position of an object traveling at constant speed clockwise around the circle.Which arrow best represents the direction of the acceleration of the object at point P?

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.)

A figure skater rotating at 5.00 rad/s with arms extended has a moment of inertia of 2.25 kg • m². If the arms are pulled in so the moment of inertia decreases to 1.80 kg • m²,what is the final angular speed?