Quiz 7: Rotational Kinetic Energy

1. Momentum is the product of ___________.

Mass times velocity

Force times distance

Speed times acceleration

Time and space

Momentum is a concept in physics that describes the quantity of motion an object possesses. It is calculated by multiplying the mass of an object by its velocity. Mass refers to the amount of matter an object contains, while velocity refers to the speed and direction of its motion. Therefore, the correct answer is "mass times velocity".

Explanation

Momentum is a concept in physics that describes the quantity of motion an object possesses. It is calculated by multiplying the mass of an object by its velocity. Mass refers to the amount of matter an object contains, while velocity refers to the speed and direction of its motion. Therefore, the correct answer is "mass times velocity".

2. The kinetic energy of an object will increase the most if you __________________.

Double the velocity of the object

Double the mass of the object

Double the potential energy

Double the temperature of the object

The kinetic energy of an object is directly proportional to its velocity squared. Therefore, if you double the velocity of the object, the kinetic energy will increase the most. This is because the kinetic energy formula, KE = 1/2mv^2, shows that the velocity has a greater impact on the kinetic energy than the mass of the object. Doubling the mass of the object would only result in a linear increase in kinetic energy, while doubling the velocity would result in a quadruple increase in kinetic energy.

Explanation

The kinetic energy of an object is directly proportional to its velocity squared. Therefore, if you double the velocity of the object, the kinetic energy will increase the most. This is because the kinetic energy formula, KE = 1/2mv^2, shows that the velocity has a greater impact on the kinetic energy than the mass of the object. Doubling the mass of the object would only result in a linear increase in kinetic energy, while doubling the velocity would result in a quadruple increase in kinetic energy.

3. A person jumps to the ground from a platform 10 feet high. Which of the following is true?

The person has more kinetic energy before they jump than after they jump.

The person has less potential energy at the top of the platform than in the air.

The person's potential energy at the instant they jump is approximately equal to their kinetic energy the instant they land.

The person's kinetic energy at the instant they jump is approximately double their potential energy the instant they land.

When the person is at the top of the platform, they have maximum potential energy due to their height. As they jump, this potential energy is converted into kinetic energy, which is the energy of motion. At the instant they jump, their potential energy is equal to their kinetic energy because energy is conserved. When they land on the ground, their kinetic energy is at its maximum while their potential energy is zero. Therefore, the person's potential energy at the instant they jump is approximately equal to their kinetic energy the instant they land.

Explanation

When the person is at the top of the platform, they have maximum potential energy due to their height. As they jump, this potential energy is converted into kinetic energy, which is the energy of motion. At the instant they jump, their potential energy is equal to their kinetic energy because energy is conserved. When they land on the ground, their kinetic energy is at its maximum while their potential energy is zero. Therefore, the person's potential energy at the instant they jump is approximately equal to their kinetic energy the instant they land.

4. When playing billiards, the collisions between the balls are best described as __________________.

Elastic

Inelastic

Expensive

Exhaustive

The collisions between the balls in billiards are best described as elastic. In an elastic collision, the kinetic energy and momentum of the balls are conserved. This means that when the balls collide, they bounce off each other without losing any energy, resulting in a predictable and efficient transfer of momentum. This is in contrast to an inelastic collision, where some of the kinetic energy is lost and the balls may stick together or deform upon impact.

Explanation

The collisions between the balls in billiards are best described as elastic. In an elastic collision, the kinetic energy and momentum of the balls are conserved. This means that when the balls collide, they bounce off each other without losing any energy, resulting in a predictable and efficient transfer of momentum. This is in contrast to an inelastic collision, where some of the kinetic energy is lost and the balls may stick together or deform upon impact.

5. If two objects collide with each other, _______________.

The sum of their momentums after the collision is equal to the sum of their momentums before the collision

The momentum before the collision is always greater than the total momentum after the collision

The object with greater mass always has greater momentum

They both lose momentum at the moment of impact

When two objects collide with each other, the law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. This means that the sum of their momentums after the collision is equal to the sum of their momentums before the collision. This principle holds true regardless of the masses of the objects or the direction of their velocities.

Explanation

When two objects collide with each other, the law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision. This means that the sum of their momentums after the collision is equal to the sum of their momentums before the collision. This principle holds true regardless of the masses of the objects or the direction of their velocities.

6. A ball rolls down a hill. The potential energy of the ball at the top of the hill is equal to...

The translational kinetic energy plus the rotational kinetic energy at the bottom of the hill

1/2 mv^2 at the bottom of the hill

It depends on the radius of the ball

Less than 1/2 mv^2 at the bottom of the hill

The potential energy of the ball at the top of the hill is converted into both translational kinetic energy and rotational kinetic energy as it rolls down the hill. Therefore, the total energy at the bottom of the hill is the sum of these two types of kinetic energy, which is represented by the answer choice "The translational kinetic energy plus the rotational kinetic energy at the bottom of the hill."

Explanation

The potential energy of the ball at the top of the hill is converted into both translational kinetic energy and rotational kinetic energy as it rolls down the hill. Therefore, the total energy at the bottom of the hill is the sum of these two types of kinetic energy, which is represented by the answer choice "The translational kinetic energy plus the rotational kinetic energy at the bottom of the hill."

7. Is the formula for:

Moment of inertia

Rotational kinetic energy

Total kinetic energy of a moving object

Potential energy of rotation

The formula for rotational kinetic energy is the correct answer. Rotational kinetic energy is the energy possessed by an object due to its rotation. It is calculated using the formula 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. This formula relates the mass distribution of the object (moment of inertia) and the rate at which it rotates (angular velocity) to its rotational kinetic energy.

Explanation

The formula for rotational kinetic energy is the correct answer. Rotational kinetic energy is the energy possessed by an object due to its rotation. It is calculated using the formula 1/2 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. This formula relates the mass distribution of the object (moment of inertia) and the rate at which it rotates (angular velocity) to its rotational kinetic energy.

8. You take an object of irregular shape and draw a big, red dot right on its center of mass. What path will the red dot trace out if you throw the object spinning through the air?

A parabola

A half-circle

An irregular path since the object is not perfectly round

You can't tell unless you know how fast the object is spinning

When the object is thrown spinning through the air, the red dot will trace out a parabolic path. This is because the object's center of mass is the point around which it rotates, and any point on the object will move in a parabolic trajectory when it is thrown. The irregular shape of the object does not affect the path traced by the red dot, as long as the dot is placed at the center of mass. The speed at which the object is spinning does not alter the fact that the path will be a parabola.

Explanation

When the object is thrown spinning through the air, the red dot will trace out a parabolic path. This is because the object's center of mass is the point around which it rotates, and any point on the object will move in a parabolic trajectory when it is thrown. The irregular shape of the object does not affect the path traced by the red dot, as long as the dot is placed at the center of mass. The speed at which the object is spinning does not alter the fact that the path will be a parabola.

9. You have 3 round objects of equal mass and equal radius, but different shapes. Which of the following shapes will have the largest moment of inertia?

A hollow ring

A solid disk

A solid sphere

They are all equal

A hollow ring will have the largest moment of inertia compared to a solid disk and a solid sphere. Moment of inertia depends on the distribution of mass around an axis of rotation. In a hollow ring, the mass is distributed farthest from the axis, resulting in a larger moment of inertia. In a solid disk, the mass is distributed closer to the axis, making the moment of inertia smaller. Similarly, in a solid sphere, the mass is distributed evenly around the axis, resulting in the smallest moment of inertia. Therefore, the hollow ring will have the largest moment of inertia.

Explanation

A hollow ring will have the largest moment of inertia compared to a solid disk and a solid sphere. Moment of inertia depends on the distribution of mass around an axis of rotation. In a hollow ring, the mass is distributed farthest from the axis, resulting in a larger moment of inertia. In a solid disk, the mass is distributed closer to the axis, making the moment of inertia smaller. Similarly, in a solid sphere, the mass is distributed evenly around the axis, resulting in the smallest moment of inertia. Therefore, the hollow ring will have the largest moment of inertia.

10. A round object is at the top of a hill. Assuming that friction does not slow it down at all, will it go down the hill faster if it just slides down without rotating, or if it rolls down?

Sliding

Rolling

If friction doesn't slow it down, then they are the same

It depends on whether or not the object is hollow

If friction does not slow it down at all, the round object will go down the hill faster if it just slides down without rotating. Rolling involves both sliding and rotation, which requires additional energy and slows down the object compared to just sliding. Therefore, if friction is not a factor, sliding will result in a faster descent down the hill.

Explanation

If friction does not slow it down at all, the round object will go down the hill faster if it just slides down without rotating. Rolling involves both sliding and rotation, which requires additional energy and slows down the object compared to just sliding. Therefore, if friction is not a factor, sliding will result in a faster descent down the hill.