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WorksheetsEnergy and Momentum of Rotating Systems Quiz
Total questions: 21
Worksheet time: 11mins
A figure skater spins with her arms extended and then pulls them close to her body. Which statement best explains why she spins faster?
The law of conservation of linear momentum
The law of conservation of angular momentum
A decrease in her moment of inertia creates torque
An increase in her rotational kinetic energy creates force
The total kinetic energy of a rolling ball includes:
Only rotational energy about its center of mass
Only translational energy of its center of mass
The sum of rotational and translational energies
The product of rotational and translational energies
A spinning flywheel slows down due to friction. This represents:
Conservation of angular momentum
An application of angular impulse
A violation of Newton's first law
Conservation of rotational energy
When comparing work done by torque, which combination would produce the same amount of work? if W=τθ
Double the torque and double the angular displacement
Half the torque and double the angular displacement
Double the torque and half the angular displacement
Double the torque and quarter the angular displacement
What happens to a rolling object's angular momentum if the reference point for rotation is changed?
It always remains exactly the same
The numerical value changes but total angular momentum is conserved
It becomes zero at certain reference points
It doubles with each change in reference point
A bowling ball is rolling without slipping. What is true about its motion?
The point of contact with the ground has zero instantaneous velocity
Kinetic friction is doing work on the ball
The ball's translational speed is independent of its rotation
The ball's total energy increases as it rolls
In terms of energy efficiency, why is rolling without slipping preferable to rolling with slipping?
Rolling without slipping requires less force
Static friction does no work in pure rolling
Rolling with slipping conserves more energy
kinetic friction adds energy to the system
How does angular impulse relate to angular momentum?
They are always equal
Angular impulse causes a change in angular momentum
They are inversely proportional
Angular impulse is the square of angular momentum
For a rigid system, which statement about rotational kinetic energy is TRUE?
It can only exist if the center of mass is moving
It must be less than translational kinetic energy
It can exist even when the center of mass is stationary
It is always equal to translational kinetic energy
A system's total angular momentum can change when:
The system's mass distribution changes
The system's rotation speed changes
An external torque acts on the system
The system's temperature changes
A spinning chair has a moment of inertia I₁ and angular velocity ω₁. If its moment of inertia changes to I₂, what is the new angular velocity ω₂ according to conservation of angular momentum?
ω₂ = (I₁/I₂)ω₁
ω₂ = (I₂/I₁)ω₁
ω₂ = I₁I₂ω₁
ω₂ = ω₁/I₁I₂
Two identical solid spheres roll down an incline. Sphere A starts from rest at height h, while sphere B starts from height h/2. At the bottom, the ratio of A's total kinetic energy to B's is:
4:1
2:1
1:1
1:2
A cylinder and a hoop of the same mass and radius roll down an incline without slipping. Which reaches the bottom first?
The cylinder
The hoop
They reach simultaneously
It depends on the incline angle
The rotational inertia of a system suddenly doubles while angular momentum remains constant. What happens to the rotational kinetic energy?
Doubles
Stays the same
Reduces by half
Reduces by one-fourth
A platform rotates freely with two students standing on opposite edges. If both students walk halfway toward the center, what happens to the platform's angular velocity?
Increases
Decreases
Remains constant
A solid sphere and a hollow sphere of identical mass and radius roll without slipping. Which has more total kinetic energy at the same angular velocity?
Solid sphere
Hollow sphere
Both have the same energy
Depends on the velocity
When a ballerina spins with arms extended and then brings them in, her rotational kinetic energy:
Remains constant
Increases
Decreases
Depends on the speed
A rotating system's angular momentum vector points:
In the direction of rotation
Perpendicular to the rotation plane
Parallel to the rotation plane
In the direction of the applied torque
For a rigid body rotating about a fixed axis, at what point is the angular velocity:
Greatest at the outer edge
Greatest at the center
The same everywhere
Varying proportionally with radius
The work-energy theorem for rotation states that work done by torque equals:
Change in potential energy
Change in rotational kinetic energy
Change in angular momentum
Change in moment of inertia
When a system's moment of inertia changes while maintaining constant angular momentum, mechanical energy is:
Always conserved
Never conserved
Conserved only if the change is gradual
Conserved only if the change is instantaneous
