6.3 Angular Momentum and Angular Impulse

• What is angular momentum defined as in rotational systems?

  Rotational equivalent of linear momentum
• What does the moment of inertia depend on in angular momentum calculations?

  Mass distribution
• Match the properties of linear and angular momentum with their definitions:

  Linear Momentum ↔️ $p =$$mv$

  Angular Momentum ↔️ $L =$$I\omega$
• The SI unit of angular momentum is derived from the formula $L =$$I\omega$


  True
• What is the SI unit for linear momentum?

  kg⋅m/s
• The angular velocity $\omega$ is measured in units of rad/s.


  True
• What is the formula for angular momentum?

  $L =$$I\omega$
• Angular impulse is mathematically expressed as $J =$$\int \tau dt =$$\Delta$ L
• How does linear impulse differ from angular impulse in terms of definition?

  Change in linear momentum vs. change in angular momentum
• What does the variable $\tau$ represent in the formula for angular impulse?


  Torque
• What is angular momentum defined as in rotational motion?

  Resistance to rotational changes
• What is the formula for angular momentum?

  L = I\omega</latex>
• The SI unit of angular momentum is derived from the formula $L =$$I\omega$, where $\omega$ represents the angular velocity
• The angular momentum unit reflects the rotational nature of the quantity.


  True
• Angular impulse connects torque to the change in angular momentum.


  True
• What is the change in angular momentum of a disk subjected to a torque of 5 N⋅m for 3 s?

  15 kg⋅m²/s
• Angular momentum is a conserved quantity in a closed system


  True
• The formula $L =$$I\omega$ is analogous to $p =$$mv$ for linear momentum


  True
• In angular momentum, the moment of inertia is analogous to mass in linear momentum

  True
• What is the unit of moment of inertia in the SI system?

  kg⋅m²
• What does the variable $L$ represent in the formula for angular momentum?


  Angular momentum
• What is the SI unit of angular momentum?

  kg⋅m²/s
• The angular momentum unit incorporates both moment of inertia and angular velocity.


  True
• What does angular impulse represent in rotational motion?

  Change in angular momentum
• Match the property with its corresponding quantity:

  Change in linear momentum ↔️ Linear impulse

  Change in angular momentum ↔️ Angular impulse
• Angular impulse is the rotational equivalent of linear impulse.

  True
• The SI unit for angular momentum is kilogram-meter squared per second
• The moment of inertia $I$ is the rotational equivalent of mass $m$ in linear momentum.


  True
• Arrange the following steps to derive the SI unit of angular momentum:

  1️⃣ Identify the formula: L = I\omega</latex>

  2️⃣ Determine the SI unit of moment of inertia: kg⋅m²

  3️⃣ Determine the SI unit of angular velocity: rad/s

  4️⃣ Multiply the units: kg⋅m² ⋅ rad/s

  5️⃣ Simplify the result: kg⋅m²/s
• What is the SI unit of angular momentum?

  kg⋅m²/s
• What is angular impulse defined as?

  Change in angular momentum
• What does the angular momentum-angular impulse theorem state?

  J = ΔL
• Match the property with its corresponding formula in linear and rotational motion:

  Momentum in linear motion ↔️ p = mv

  Momentum in rotational motion ↔️ L = Iω

  Impulse in linear motion ↔️ I = ∫F dt = Δp

  Impulse in rotational motion ↔️ J = ∫τ dt = ΔL
• What quantity affects linear momentum in contrast to angular momentum?

  Force
• Angular momentum measures an object's resistance to changes in its rotational motion.
• What are the three variables in the formula $L =$$I\omega$?


  Angular momentum, moment of inertia, angular velocity
• Place the following quantities in order from their corresponding units:

  1️⃣ Linear Momentum (kg⋅m/s)

  2️⃣ Angular Momentum (kg⋅m²/s)
• The variable $I$ in the formula for angular momentum stands for the moment of inertia
• The SI unit of angular momentum is the kilogram-meter squared per second
• What is angular impulse the rotational equivalent of?

  Linear impulse