Conservation of Angular Momentum Questions

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Very Short Answers Questions [1 Mark Questions]

Ques. A man standing on a revolving platform spreads his hands outward, then

1. Angular momentum increases
2. Angular momentum is zero
3. Angular velocity increases
4. Angular velocity decreases

Ans. The correct answer is d. Angular velocity decreases

Explanation: When the man spreads his hands outward, his moment of inertia increases. Since angular momentum is conserved, his angular velocity must decrease.

Ques. A dancer standing on the rotating table with his hands lowered. When he outstretches his hands, the angular momentum of the dancer

1. Decreases
2. Increases
3. Remains constant
4. None of the above

Ans. The correct answer is c. Remains constant

Explanation: When the dancer standing on the rotating table stretches his hands his moment of inertia increases and angular velocity decreases to conserve the angular momentum. Hence the angular momentum of the dancer remains constant.

Ques. A solid sphere is rotating freely about its symmetry axis in free space. The radius of the sphere is increased keeping its mass the same. Which of the following physical quantities would remain constant for the sphere?

1. Moment of inertia
2. Angular momentum
3. Angular velocity
4. None of the above

Ans. The correct answer is b. Angular momentum

Explanation: When the radius of the sphere increases, its particle will go farther away from the center of rotation, therefore its moment of inertia will increase. The angular momentum of the sphere will remain conserved.

Ques. Angular momentum is a

1. Vector quantity
2. Scalar quantity
3. Dimensionless quantity
4. None of the above

Ans. The correct answer is a. Vector quantity

Explanation: The angular momentum of a body is a vector quantity since it has both magnitude and direction.

Ques. If a body of mass m is moving with a velocity v, then the formula to find the momentum p is

1. p = m + v
2. p = m/v
3. p = m²v
4. p = mv

Ans. The correct answer is d. p = mv

Explanation: Linear momentum of a body is the product of its mass and velocity, therefore it is given by p = mv.

Ques. If a body is rotating in a circular path of radius r having linear momentum p, then the formula of angular momentum L is

1. L = rp
2. L = r - p
3. L = r + p
4. L = r/p

Ans. The correct answer is a. L = rp

Explanation: The relation between angular momentum and linear momentum is L = rp. Where r is the radius of the circular path.

Ques. What is the unit of momentum?

1. Kg m/s²
2. Kg m²/s
3. Kg m/s
4. Kg m²/s²

Ans. The correct answer is c. Kg m/s

Explanation: The unit of momentum is Kg m/s.

Ques. Is the law of conservation of angular momentum applied in electric generators?

1. Yes
2. No

Ans. The correct answer is a. Yes

Explanation: The law of conservation of angular momentum has several applications such as electric generators and aircraft engines.

Ques. If the net torque is zero, then angular momentum is

1. 1
2. -1
3. Infinity
4. Constant

Ans. The correct answer is d. Constant

Explanation: When the torque on a system is zero, the angular momentum is constant and so conserved.

Ques. The doors are provided with handles near the outer edges far away from the hinges

1. to exert minimum torque on the door to open it easily.
2. to exert maximum torque on the door to open it easily.
3. because while opening the door fingers are not hurt by hinges.
4. because the position does not matter and is convenient to fix at the outer edge.

Ans. The correct answer is a. to exert minimum torque on the door to open it easily.

Explanation: The doors are provided with handles near the outer edges and far away from the hinges to maximize the lever arm. This makes it easier to open the door by reducing the amount of force required. 

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Short Answers Questions [2 Marks Questions]

Ques. Define angular momentum.

Ans. Angular Momentum is the property of rotating objects that is determined by the product of their moment of inertia and angular velocity.

Ques. What is the conservation of angular momentum?

Ans. Conservation of angular momentum is an inherent characteristic of a rotating system in which the angular momentum of a system remains constant until acted on by an external torque. In other words, the angular momentum will remain constant as long as the net torque acting on the system is zero.

Ques. Define linear momentum.

Ans. Linear momentum is a measure of the amount of motion contained in a body, and it is determined by the mass of the object and its velocity.

Ques. What is the relation between linear & angular momentum?

Ans. Consider a particle of mass m and a linear momentum p at a position \(\vec{r}\) from the origin. The angular momentum \(\vec{L}\)L of the particle with respect to the origin is defined as the cross product of \(\vec{r}\) and \(\vec{p}\).

\(\vec{L} = \vec{r} \times \vec{p} =rp sin \theta\)

Where θ is the angle between \(\vec{r}\) and \(\vec{p}\).

Ques. What is angular momentum for an extended object?

Ans. The formula of angular momentum for an extended object is given by

\(\vec{L} = \vec{I} \times \vec{\omega}\)

Where

• I is the moment of inertia of the rotating object
• ω is the angular velocity

Ques. What is the moment of inertia?

Ans. The moment of inertia of a rigid body, also known as its mass moment of inertia, angular mass, second moment of mass, or, more precisely, rotational inertia, is a quantity that determines the torque required for a desired angular acceleration about a rotational axis, similarly to how mass determines the force required for a desired acceleration.

Ques. Define angular velocity.

Ans. The angular velocity, also known as the angular frequency vector, is a pseudovector representation of how the angular position or direction varies with time, i.e. how quickly an object rotates around an axis of rotation and how quickly the axis itself changes direction.

Ques. What is the dimensional formula of angular momentum?

Ans. The dimensional formula of angular momentum is given by

[L] = [M L² T^-1]

Ques. Define torque.

Ans. A torque is a rotational force that causes an object to rotate around an axis. It is defined as the product of force and the perpendicular distance between the line of action of force and the axis of rotation.

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Long Answers Questions [3 Marks Questions]

Ques. A car of mass 300 kg is traveling on a circular track of radius 100 m with a constant speed of 60 m/s. Calculate the angular momentum of the car about the center of the circle.

Ans. Given

• The mass of the car, m = 300 kg
• The radius of the circular track, r = 100 m
• Speed of the car, v = 60 m/s

The angular momentum of the car is given by

L = rp sinθ

Where

• p is the momentum of the car
• θ is the angle between r and p

In this case θ = 90°

⇒ L = rp

But momentum, p = mv

⇒ L = rmv

On substituting the values, we get

L = 100 x 300 x 60 = 18 x 10⁵ kg m²/s.

Ques. A torque of 10 N^-m is applied on a wheel having an angular momentum of 2 kg m²/s. Calculate the angular momentum of the wheel after 4 seconds.

Ans. Given

• Torque applied to the wheel, τ = 10 N^-m
• Initial angular momentum, L₁ = 2 kg m²/s

Let L₂ be the final angular momentum of the wheel after 4 seconds, then

Torque, τ = (L₂ - L₁)/t

⇒ L₂ = τt + L₁

On substituting the values, we get

L₂ = (10 x 4) + 2 = 42 kg m²/s

Hence the angular momentum of the wheel after 4 seconds is 42 kg m²/s.

Ques. What is the difference between linear momentum and angular momentum?

Ans. The following are the differences between linear momentum and angular momentum

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Very Long Answers Questions [5 Marks Questions]

Ques. What are the applications of conservation of angular momentum?

Ans. The following are the applications of conservation of angular momentum

• An ice skater performs the feasts using the conservation of momentum. Assume that the ice skater is spinning with her arms and legs outstretched. Her moment of inertia decreases and her angular velocity increases as she folds her arms and pulls her extended legs closer together.
• The conservation of angular momentum is also used to ensure that riders are not thrown from roller coasters and other amusement park rides.
• The angular velocity of the revolution of a planet around the sun in an elliptical orbit increases as the planet approaches the sun, and vice versa. This is because as the planet gets closer to the sun, its moment of inertia about the sun decreases, and therefore its angular velocity increases.
• When a diver rolls their body into a ball before hitting the water, their moment of inertia decreases, allowing them to spin faster.

Ques. A rod of mass 3 kg and length 2 m is pivoted at one end A and kept on a smooth surface. A particle of mass 500 gm strikes the other end B of the rod and sticks to the rod. If the particle was moving with the speed of 20 m/s, what is the angular speed of the rod after collision?

Ans. Given

• The mass of the rod, m₁ = 3 kg
• The mass of the particle strikes the end B of the rod, m₂ = 500 gm = 0.5 kg
• Length of the rod = radius of the circular path, r = 2 m
• The initial linear speed of the particle, v = 20 ms

Initial angular momentum is given by

L_i = m₂vr

⇒ L_i = 0.5 x 20 x 2 = 20 kg m²/s

The final angular momentum is given by

L_f = I_Aω

Where 

• I_A is the moment of inertia about point A
• ω is the angular speed of the rod after collision

⇒ L_f = [m₁l²/3 + m₂l²]ω

On substituting the values, we get

⇒ L_f = [4 + 2]ω = 6ω

Since the rod is pivoted at point A, the angular momentum of the rod and particle system can only be conserved about point A. Therefore

L_i = L_f

⇒ 2 = 6ω

⇒ ω = 0.33 rad/s

Hence the angular speed of the rod after the collision is 0.33 rad/s.

Ques. A bus of mass 800 kg is traveling on a circular track of radius 50 m with a constant speed of 80 m/s. Calculate the angular momentum about the center of the circle.

Ans. Given

• The mass of the bus, m = 800 kg
• The radius of the circular track, r = 50 m
• Speed of the car, v = 80 m/s

The linear momentum of the bus is given by

p = mv

⇒ p = 800 x 80 = 64000 kg m/s

The angular momentum of the car is given by

L = rp sinθ

Where

• L is the angular momentum
• r is the radius of the circular track
• p is the linear momentum of the object
• θ is the angular between r and p.

On substituting the values, we get

L = 50 x 64000 x sin 90

⇒ L = 3.2 x 10⁶ kgm²/s

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