5.4 Angular Momentum

• The formula relating torque and angular momentum is $\tau =$$\frac{dL}{dt}$, where torque is the rate of change of angular momentum
• What happens to angular momentum if no external torque acts on a system?

  It remains constant
• Match the term with its definition in the context of angular momentum:

  Rotational inertia ↔️ Resistance to changes in rotation

  Angular velocity ↔️ Rate at which an object rotates

  Torque ↔️ External force causing rotation
• If an object's rotational inertia decreases, its angular velocity must increase to conserve angular momentum.
• What is angular momentum analogous to in linear motion?

  Linear momentum
• What is angular momentum the rotational equivalent of?

  Linear momentum
• The formula for angular momentum (L) is Iω
• Rotational inertia reflects an object's resistance to changes in rotation.
• What does angular velocity measure?

  How fast the object rotates
• Match the property with its corresponding concept:

  Mass x Velocity ↔️ Linear Momentum

  Rotational Inertia x Angular Velocity ↔️ Angular Momentum
• Angular momentum is conserved unless external torque is applied.
• Angular momentum measures an object's resistance to changes in its rotational motion.
• What are the components of angular momentum in its formula?

  I and ω
• Match the concept with its formula:

  Linear Momentum ↔️ $p =$$mv$

  Angular Momentum ↔️ $L =$$I \omega$
• The unit for angular momentum is kg⋅m²/s, whereas the unit for linear momentum is kg⋅m/s
• What does moment of inertia depend on?

  Mass distribution
• What is angular momentum the rotational equivalent of?

  Linear momentum
• Angular momentum is a measure of an object's resistance to changes in its rotational motion.
• The angular momentum (L) of an object is calculated as Iω
• Match the variable with its description:

  I ↔️ Rotational inertia

  ω ↔️ Angular velocity

  L ↔️ Angular momentum
• Angular momentum is conserved unless an external torque is applied to the object.
• Rotational inertia is a measure of an object's resistance to changes in rotation
• Match the shape with its moment of inertia formula:

  Solid Cylinder ↔️ $I =$$\frac{1}{2} m r^{2}$

  Sphere ↔️ $I =$$\frac{2}{5} m r^{2}$

  Hollow Cylinder ↔️ $I =$$m r^{2}$
• The moment of inertia is larger for objects with mass concentrated farther from the axis of rotation.
• What is another name for moment of inertia?

  Rotational inertia
• Moment of inertia measures an object's resistance to changes in rotational motion
• The moment of inertia depends on the mass distribution of the object relative to the pivot point.
• What is the formula for moment of inertia?

  $I =$$\sum m_{i} r_{i}^{2}$
• Match the shape with its moment of inertia formula:

  Solid Cylinder ↔️ $I =$$\frac{1}{2} m r^{2}$

  Hollow Cylinder ↔️ $I =$$m r^{2}$

  Sphere ↔️ $I =$$\frac{2}{5} m r^{2}$
• What happens to the moment of inertia if the mass is concentrated farther from the axis?

  It increases
• Angular momentum is the rotational equivalent of linear momentum
• What is the formula for angular momentum?

  $L =$$I \omega$
• Angular momentum is conserved in a closed system unless an external torque is applied.
• Angular momentum measures an object's resistance to changes in its rotational motion
• What does 'I' represent in the angular momentum formula?

  Rotational inertia
• Torque is required to change angular momentum.
• What is the formula relating torque and angular momentum?

  $\tau =$$\frac{dL}{dt}$
• If there is no external torque acting on a system, its angular momentum remains constant
• What does rotational inertia represent in rotational motion?

  Resistance to rotation
• Angular velocity is analogous to linear velocity