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What is Angular Momentum (L) for a point particle?

$L = r \times p = r m v \sin(\theta)$

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What is Angular Momentum (L) for a point particle?

$L = r \times p = r m v \sin(\theta)$

What is Angular Momentum (L) for an extended object?

$L = I \omega$

Define Conservation of Angular Momentum.

The total angular momentum of a system remains constant unless acted upon by a net external torque.

What is the relationship between torque and angular momentum?

$\tau = \frac{dL}{dt}$

Define moment of inertia.

A measure of an object's resistance to changes in its rotation.

What is torque?

A rotational force that causes a change in angular momentum.

What are the key differences between linear and angular momentum?

Linear Momentum: $p=mv$ , translational motion | Angular Momentum: $L=I\omega$ , rotational motion

Differentiate between elastic and inelastic collisions in the context of angular momentum.

Elastic: Kinetic energy is conserved, Angular momentum is conserved | Inelastic: Kinetic energy is not conserved, Angular momentum is conserved

What are the steps to solve a ballistic pendulum problem?

Use conservation of linear momentum during the collision: $m_1v_1 = (m_1 + m_2)v_f$ . 2. Use conservation of energy for the swing: $\frac{1}{2}(m_1 + m_2)v_f^2 = (m_1 + m_2)gh$ .

Describe the process of angular momentum conservation in disk collisions.

Identify the system as the colliding disks. 2. Recognize that the torques are internal. 3. Apply $L_{initial} = L_{final}$ using $L=I\omega$ for each disk.

How do you approach a problem involving a changing moment of inertia?

Recognize that angular momentum is conserved. 2. Apply $L_{initial} = L_{final}$ . 3. Express L as $I\omega$ and solve for the unknown angular velocity or moment of inertia.

All Flashcards

What is Angular Momentum (L) for a point particle?

$L = r \times p = r m v \sin(\theta)$

What is Angular Momentum (L) for an extended object?

$L = I \omega$

Define Conservation of Angular Momentum.

The total angular momentum of a system remains constant unless acted upon by a net external torque.

What is the relationship between torque and angular momentum?

$\tau = \frac{dL}{dt}$

Define moment of inertia.

A measure of an object's resistance to changes in its rotation.

What is torque?

A rotational force that causes a change in angular momentum.

What are the key differences between linear and angular momentum?

Linear Momentum: $p=mv$ , translational motion | Angular Momentum: $L=I\omega$ , rotational motion

Differentiate between elastic and inelastic collisions in the context of angular momentum.

Elastic: Kinetic energy is conserved, Angular momentum is conserved | Inelastic: Kinetic energy is not conserved, Angular momentum is conserved

What are the steps to solve a ballistic pendulum problem?

Use conservation of linear momentum during the collision: $m_1v_1 = (m_1 + m_2)v_f$ . 2. Use conservation of energy for the swing: $\frac{1}{2}(m_1 + m_2)v_f^2 = (m_1 + m_2)gh$ .

Describe the process of angular momentum conservation in disk collisions.

Identify the system as the colliding disks. 2. Recognize that the torques are internal. 3. Apply $L_{initial} = L_{final}$ using $L=I\omega$ for each disk.

How do you approach a problem involving a changing moment of inertia?

Recognize that angular momentum is conserved. 2. Apply $L_{initial} = L_{final}$ . 3. Express L as $I\omega$ and solve for the unknown angular velocity or moment of inertia.