# College Physics Reasoning and Relationships

Physics & Astronomy

## Quiz 9 :

Energy and Momentum of Rotational Motion

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Two spheres, one with the center core up to r = R/2 hollow and the other solid, have the same mass M and same outer radius R. If they are both rolling at the same linear speed, which one has the greater kinetic energy?

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B

A ventilation fan with a moment of inertia of 0.034 has a net torque of 0.11 N m applied to it. If it starts from rest, what kinetic energy will it have 10 s later?

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B

The total kinetic energy of a baseball thrown with a spinning motion is a function of:

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C

A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 10

^{}^{2}, and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 3.0 m/s, what is its total kinetic energy? Multiple Choice

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A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder, with crank, at the top of a well. The moment of inertia of the cylinder and crank is 0.21 kg m

^{2}. The bucket is raised to the top of the well and released to fall back into the well. What is the kinetic energy of the cylinder and crank at the instant the bucket is moving with a speed of 6.0 m/s? Multiple Choice

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A gyroscope has a moment of inertia of 0.14 and an initial angular speed of 30 rad/s. Friction in the bearings causes its speed to reduce to zero in 30 s. What is the value of the average frictional torque?

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A gyroscope has a moment of inertia of 0.140 kg m

^{2 }and has an initial angular speed of 12.0 rad/s. If a lubricant is applied to the bearings of the gyroscope so that frictional torque is reduced to 2.00 10^{}^{2}N M, then in what time interval will the gyroscope coast from 12.0 rad/s to zero? Multiple Choice

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A cylinder with its mass concentrated toward the center has a moment of inertia of 0.2MR

^{2}. If this cylinder is rolling without slipping along a level surface with a linear speed v, what is the ratio of its rotational kinetic energy to its linear kinetic energy? Multiple Choice

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A hoop with mass, M, and radius, R, rolls along a level surface without slipping with a linear speed, v. What is the ratio of rotational to linear kinetic energy? (For a hoop, .)

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A rotating flywheel can be used as a method to store energy. If it is required that such a device be able to store up to a maximum of 2.00 10

^{6}J when rotating at 400 rad/s, what moment of inertia is required? Multiple Choice

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A rotating flywheel can be used as a method to store energy. If it has 2.0 10

^{6}J of kinetic energy when rotating at 400 rad/s, and if a frictional torque of 4.0 N m acts on the system, in what interval of time would the flywheel come to rest? Multiple Choice

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An initially installed flywheel can store 10

^{6}J of kinetic energy when rotating at 300 rad/s. It is replaced by another flywheel of the same size but made of a stronger material. If its mass is the same as that of the original, and it is now capable of achieving a rotational speed of 600 rad/s, what maximum energy can be stored? Multiple Choice

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A bus is designed to draw its power from a rotating flywheel that is brought up to its maximum speed (3000 rpm) by an electric motor. The flywheel is a solid cylinder of mass 250 kg and radius 0.500 m (I

_{cylinder}= MR^{2}/2). If the bus requires an average power of 10.0 kW, how long will the flywheel rotate? Multiple Choice

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A solid sphere, a solid cylinder, and a hoop each have the same mass and radius. If they are spinning at the same angular velocity, which one has the greatest rotational kinetic energy?

Multiple Choice

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The Earth's density increases with depth. If instead the Earth had uniform density, but the same angular velocity and mass, how would its rotational kinetic energy compare to the actual value?

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A non-uniform round object of mass M and radius R is found to have its total kinetic energy to be given by when rolling down an incline. What is this object's moment of inertia?

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A hoop, solid sphere, and solid cylinder each have the same mass and same radius.When rolling down the same incline, which has the greatest torque from gravity on it?

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Three disks have the same mass and the same total kinetic energy. Disk #1 has radius R, disk #2 has radius 2R, and disk #3 has radius 3R. Which one has the highest ?

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A box slides down a frictionless incline, and a hoop rolls down another incline. Both inclines have the same height, and both the box and the hoop have the same mass. If both objects start from rest, upon reaching the bottom of the incline which one will have the greater kinetic energy and which one will have the greater speed?

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A solid sphere of mass 2.5 kg and radius 0.12 m is at rest at the top of a ramp inclined 15. It rolls to the bottom without slipping. The upper end of the ramp is 1.2 m higher than the lower end. Find the sphere's total kinetic energy when it reaches the bottom.

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