Question 1

The angular momentum of a body about a particular axis as a function of time is shown in the graph.The external torque acting on the body along this axis at t = 2 s is

Accepted Answer

The answer of The angular momentum of a body about...

Question 2

An athletic can twirl a baton so that it reaches an angular velocity of 12 rad/s from rest in 0.5 s.If the length of a uniform baton is 0.8 m and the mass is 0.5 kg,what is the torque needed to reach the angular velocity?

Accepted Answer

The moment of inertia of a uniform baton of length L and mass M rotating about its center is:

I = (1/12)ML^2

Using this moment of inertia, we can calculate the torque required to reach the angular velocity:

τ = Iα = (1/12)ML^2(ωf - ωi)/t

where ωi = 0 is the initial angular velocity.

Plugging in the given values, we get:

τ = (1/12)(0.5 kg)(0.8 m)^2(12 rad/s)/0.5 s

τ = 0.64 Nm

Therefore, the answer is D) 0.64 Nm.

Question 3

A wheel is rotating freely with an angular speed of 20 rad/s on a shaft whose moment of inertia is negligible.A second identical wheel,initially at rest,is suddenly coupled to the same shaft.The angular speed of the coupled wheels is

Accepted Answer

The angular momentum before and after coupling remains constant due to the conservation of angular momentum. Since the moment of inertia doubles when the second identical wheel is added, the angular speed halves to 10 rad/s.

Question 4

A woman sits on a spinning piano stool with her arms folded.When she extends her arms,which of the following occurs?

Accepted Answer

When the woman extends her arms, she increases her moment of inertia, which is the measure of an object's resistance to change in its rotational motion. As a result, her angular speed decreases to conserve angular momentum, which is equal to the product of moment of inertia and angular speed. This conservation law implies that when moment of inertia increases, angular speed decreases and vice versa.

Question 5

The angular momentum vector for a spinning wheel lies along its axle and is pointed east.To make this vector point south,it is necessary to exert a force on the east end of the axle in which direction?

Accepted Answer

Applying a force upward on the east end of the axle will create a torque that changes the direction of the angular momentum vector from east to south.

Question 6

A man turns with an angular velocity on a rotating table,holding two equal masses at arms' length.If he drops the two masses without moving his arms,his angular velocity

Accepted Answer

The man's angular velocity remains the same because dropping the masses without moving his arms does not change the moment of inertia of the system, and thus, by the conservation of angular momentum, his angular velocity remains unchanged.

Question 7

A merry-go-round with a moment of inertia of 6.78 $\times$ 10³ kg · m² is coasting at 2.20 rad/s.When a 72.6-kg man steps onto the rim,the angular velocity decreases to 2.0 rad/s.The radius of the merry-go-round is

Accepted Answer

Explanation:The angular momentum of the system is conserved, so:$$I_i\omega_i = I_f\omega_f$$$$(6.78	imes10^3 	ext{ kg$\cdot$m}^2)(2.20 	ext{ rad/s}) = (6.78	imes10^3 	ext{ kg$\cdot$m}^2 + 72.6 	ext{ kg}r^2)(2.00 	ext{ rad/s})$$$$r = 3.06 	ext{ m}$$

Question 8

Two identical cylindrical discs have a common axis.Initially one of the discs is spinning.When the two discs are brought into contact,they stick together.Which of the following is true?

Accepted Answer

The total angular momentum is conserved because there are no external torques. However, kinetic energy is not conserved due to inelastic collision, and it is reduced to one-quarter of its original value when the two discs stick together and rotate as one.

Question 9

A hoop rotates about an axis through its center with an angular velocity of 40.0 rad/s.If the rotational kinetic energy of the hoop is 400 J,its angular momentum is

Accepted Answer

The answer of A hoop rotates about an axis through...

Question 10

In a playground there is a small merry-go-round of radius 1.25 m and mass 175 kg.Assume the merry-go-round to be a uniform disc.A child of mass 45 kg runs at a speed of 3.0 m/s tangent to the rim of the merry-go-round (initially at rest)and jumps on.If we neglect friction,what is the angular speed of the merry-go-round after the child has jumped on and is standing at its outer rim?

Accepted Answer

The initial angular momentum of the system is due to the child running, which is m*v*r. The final angular momentum is the sum of the angular momentum of the child and the merry-go-round. Using conservation of angular momentum: m*v*r = (I_merry-go-round + I_child)*ω. Solving for ω gives 0.82 rad/s.

Question 11

A woman sits on a stool that can turn friction-free about its vertical axis.She is handed a spinning bicycle wheel that has angular momentum ₀ and she turns it over (that is,through 180º).She thereby acquires an angular momentum of magnitude

Accepted Answer

The answer of A woman sits on a stool that...

Question 12

Which of the following are required for the total momentum (both angular and linear)of a system to be conserved?

Accepted Answer

The answer of Which of the following are required for...

Question 13

Two balls,each of mass m,are attached to the ends of a rod of length l and mass M.The system is then rotated about a frictionless pivot located at the center of mass with angular velocity $\omega$.The angular momentum of the system in vector form about the pivot is

Accepted Answer

The answer of Two balls,each of mass m,are attached to...

Question 14

A man is walking north carrying a suitcase that contains a spinning gyroscope mounted on an axle attached to the front and back of the case.The angular velocity of the gyroscope points north.The man now begins to turn to walk east.As a result,the front end of the suitcase

Accepted Answer

The answer of A man is walking north carrying a...

Question 15

If the sum of the external torques acting on an isolated system of particles is zero,it must be true that

Accepted Answer

The conservation of angular momentum states that if the sum of the external torques acting on an isolated system of particles is zero, then the angular momentum of the system does not change. The other options are not necessarily true. The system may still have kinetic and/or linear velocity, and the angular momentum may not be continually decreasing.

Question 16

A man stands on the center of a platform that is rotating on frictionless bearings at a speed of 1.00 rad/s.Originally his arms are outstretched and he holds a 4.54-kg mass in each hand.He then pulls the weights in toward his body.Assume the moment of inertia of the man,including his arms,to remain constant at 5.42 kg · m².If the original distance of the weights from the axis is 0.914 m and their final distance is 0.305 m,the final angular velocity is

Accepted Answer

The conservation of angular momentum states that the initial angular momentum equals the final angular momentum. Initially, the angular momentum is the sum of the man's moment of inertia and the weights' moment of inertia times the angular velocity. When the weights are pulled in, their moment of inertia decreases, increasing the angular velocity. Calculating gives a final angular velocity of 2.08 rad/s.

Question 17

A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min.After the power is shut off,a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later.What was the stone's initial kinetic energy when the power was turned off?

Accepted Answer

The initial kinetic energy of the grindstone can be calculated using the formula for the kinetic energy of a rotating object, $KE = \frac{1}{2}I\omega^2$, where $I$ is the moment of inertia and $\omega$ is the angular velocity in radians per second. For a disc, $I = \frac{1}{2}mr^2$, and $\omega = 600 \times \frac{2\pi}{60}$ because there are $2\pi$ radians in a revolution and 60 seconds in a minute. Plugging in the values, $I = \frac{1}{2} \times 3.0 \times (0.08)^2 = 0.0096 \, \text{kg} \cdot \text{m}^2$, and $\omega = 10\pi \, \text{rad/s}$. Therefore, $KE = \frac{1}{2} \times 0.0096 \times (10\pi)^2 \approx 15 \, \text{J}$. However, given the options do not directly match this calculation, it seems there might have been a misunderstanding or misprint in the options or the calculation process. The correct approach involves calculating the kinetic energy with the given formula, but without the exact numbers matching any of the options, the closest or intended correct answer cannot be accurately determined from the calculation provided. The initial explanation aimed to demonstrate the correct approach to finding the kinetic energy of a rotating object like a grindstone.

Question 18

If the sum of the torques on a body about a fixed axis is not zero,the body most certainly

Accepted Answer

If the sum of the torques on a body about a fixed axis is not zero, it means that there is a net torque acting on the body. According to Newton's second law of motion for rotational motion, a net torque will cause an angular acceleration in the body. Therefore, the correct choice is B, which states that the body experiences angular acceleration.

Question 19

A spinning bicycle wheel is supported as shown by a line fastened to one end of its axle.The resultant torque acting on the wheel lies along which of the following axes?

Accepted Answer

The answer of A spinning bicycle wheel is supported as...

Question 20

If the sum of the external torques on a system is zero,there is

Accepted Answer

If the sum of the external torques on a system is zero, then according to the principle of conservation of angular momentum, there will be no change in the system's angular momentum. This means that the system will maintain its original angular momentum, and there will be no change in its rotational motion. Therefore, option D is the correct choice. Option A is incorrect because a zero net external torque implies no change in moment of inertia. Option B is not an optimal choice because even though the answer is true, it does not give a direct answer to the question. Option C is not correct because there is no change in angular momentum in this case. Option E is not a valid choice because the question does not mention anything about a precessional angular velocity.

Quiz 10: Conservation of Angular Momentum

The angular momentum of a body about a particular axis as a function of time is shown in the graph.The external torque acting on the body along this axis at t = 2 s is

An athletic can twirl a baton so that it reaches an angular velocity of 12 rad/s from rest in 0.5 s.If the length of a uniform baton is 0.8 m and the mass is 0.5 kg,what is the torque needed to reach the angular velocity?

A wheel is rotating freely with an angular speed of 20 rad/s on a shaft whose moment of inertia is negligible.A second identical wheel,initially at rest,is suddenly coupled to the same shaft.The angular speed of the coupled wheels is

A woman sits on a spinning piano stool with her arms folded.When she extends her arms,which of the following occurs?

The angular momentum vector for a spinning wheel lies along its axle and is pointed east.To make this vector point south,it is necessary to exert a force on the east end of the axle in which direction?

A man turns with an angular velocity on a rotating table,holding two equal masses at arms' length.If he drops the two masses without moving his arms,his angular velocity

A merry-go-round with a moment of inertia of 6.78 $\times$ 10³ kg · m² is coasting at 2.20 rad/s.When a 72.6-kg man steps onto the rim,the angular velocity decreases to 2.0 rad/s.The radius of the merry-go-round is

Two identical cylindrical discs have a common axis.Initially one of the discs is spinning.When the two discs are brought into contact,they stick together.Which of the following is true?

A hoop rotates about an axis through its center with an angular velocity of 40.0 rad/s.If the rotational kinetic energy of the hoop is 400 J,its angular momentum is

A woman sits on a stool that can turn friction-free about its vertical axis.She is handed a spinning bicycle wheel that has angular momentum ₀ and she turns it over (that is,through 180º) .She thereby acquires an angular momentum of magnitude

Which of the following are required for the total momentum (both angular and linear) of a system to be conserved?

A man is walking north carrying a suitcase that contains a spinning gyroscope mounted on an axle attached to the front and back of the case.The angular velocity of the gyroscope points north.The man now begins to turn to walk east.As a result,the front end of the suitcase

If the sum of the external torques acting on an isolated system of particles is zero,it must be true that

A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min.After the power is shut off,a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later.What was the stone's initial kinetic energy when the power was turned off?

If the sum of the torques on a body about a fixed axis is not zero,the body most certainly

A spinning bicycle wheel is supported as shown by a line fastened to one end of its axle.The resultant torque acting on the wheel lies along which of the following axes?

If the sum of the external torques on a system is zero,there is

Quiz 10: Conservation of Angular Momentum

The angular momentum of a body about a particular axis as a function of time is shown in the graph.The external torque acting on the body along this axis at t = 2 s is

An athletic can twirl a baton so that it reaches an angular velocity of 12 rad/s from rest in 0.5 s.If the length of a uniform baton is 0.8 m and the mass is 0.5 kg,what is the torque needed to reach the angular velocity?

A wheel is rotating freely with an angular speed of 20 rad/s on a shaft whose moment of inertia is negligible.A second identical wheel,initially at rest,is suddenly coupled to the same shaft.The angular speed of the coupled wheels is

A woman sits on a spinning piano stool with her arms folded.When she extends her arms,which of the following occurs?

The angular momentum vector for a spinning wheel lies along its axle and is pointed east.To make this vector point south,it is necessary to exert a force on the east end of the axle in which direction?

A man turns with an angular velocity on a rotating table,holding two equal masses at arms' length.If he drops the two masses without moving his arms,his angular velocity

A merry-go-round with a moment of inertia of 6.78 ×\times× 103 kg · m2 is coasting at 2.20 rad/s.When a 72.6-kg man steps onto the rim,the angular velocity decreases to 2.0 rad/s.The radius of the merry-go-round is

Two identical cylindrical discs have a common axis.Initially one of the discs is spinning.When the two discs are brought into contact,they stick together.Which of the following is true?

A hoop rotates about an axis through its center with an angular velocity of 40.0 rad/s.If the rotational kinetic energy of the hoop is 400 J,its angular momentum is

A woman sits on a stool that can turn friction-free about its vertical axis.She is handed a spinning bicycle wheel that has angular momentum 0 and she turns it over (that is,through 180º) .She thereby acquires an angular momentum of magnitude

Which of the following are required for the total momentum (both angular and linear) of a system to be conserved?

Two balls,each of mass m,are attached to the ends of a rod of length l and mass M.The system is then rotated about a frictionless pivot located at the center of mass with angular velocity ω\omegaω .The angular momentum of the system in vector form about the pivot is

A man is walking north carrying a suitcase that contains a spinning gyroscope mounted on an axle attached to the front and back of the case.The angular velocity of the gyroscope points north.The man now begins to turn to walk east.As a result,the front end of the suitcase

If the sum of the external torques acting on an isolated system of particles is zero,it must be true that

A disc-shaped grindstone of mass 3.0 kg and radius 8.0 cm is spinning at 600 rev/min.After the power is shut off,a man continues to sharpen his axe by holding it against the grindstone until it stops 10 s later.What was the stone's initial kinetic energy when the power was turned off?

If the sum of the torques on a body about a fixed axis is not zero,the body most certainly

A spinning bicycle wheel is supported as shown by a line fastened to one end of its axle.The resultant torque acting on the wheel lies along which of the following axes?

If the sum of the external torques on a system is zero,there is

A merry-go-round with a moment of inertia of 6.78 $\times$ 10³ kg · m² is coasting at 2.20 rad/s.When a 72.6-kg man steps onto the rim,the angular velocity decreases to 2.0 rad/s.The radius of the merry-go-round is

A woman sits on a stool that can turn friction-free about its vertical axis.She is handed a spinning bicycle wheel that has angular momentum ₀ and she turns it over (that is,through 180º) .She thereby acquires an angular momentum of magnitude