11.1 Rotational dynamics

• What is the study of objects rotating around a fixed axis called?

  Rotational dynamics
• Angular velocity is the rate of change of angular displacement.

  True
• Match the rotational motion property with its linear motion equivalent:

  Angular displacement ↔️ Linear displacement

  Angular velocity ↔️ Linear velocity

  Angular acceleration ↔️ Linear acceleration
• Angular acceleration is the rotational equivalent of linear acceleration.


  True
• The measure of an object's resistance to changes in rotational motion is called its moment of inertia
• Match the property with its units:

  Torque ↔️ N⋅m

  Moment of inertia ↔️ kg⋅m^2
• What is the rotational equivalent of linear acceleration?

  Angular acceleration
• Torque determines the angular acceleration of an object.

  True
• Match the property with its description:

  Torque ↔️ Rotational force

  Moment of Inertia ↔️ Resistance to rotational motion
• Angular momentum is the product of moment of inertia and angular velocity
• The angle an object rotates through is called its angular displacement
• What is the rate of change of angular velocity called?

  Angular acceleration
• The rotational equivalent of linear velocity is angular velocity
• What is the rotational force that causes an object to rotate around a fixed axis called?

  Torque
• The units of torque are N⋅m.


  True
• The key quantity in rotational dynamics that describes the rate of change of angular displacement is angular velocity
• Torque is defined as rotational force
• Torque depends on force and distance from the axis
• What is the formula for angular acceleration?

  $α =$ \frac{\Deltaω}{\Deltat}
• The formula for angular momentum is $L =$$Iω$.


  True
• Angular momentum is measured in kg⋅m²/s, which represents kilogram meter squared per second
• What is the formula for rotational kinetic energy?

  $K_{r} =$$\frac{1}{2}I\omega^{2}$
• Match the type of energy with its formula:

  Rotational Kinetic Energy ↔️ $K_{r} =$$\frac{1}{2}I\omega^{2}$

  Linear Kinetic Energy ↔️ $K_{l} =$$\frac{1}{2}mv^{2}$
• What is the formula for conservation of angular momentum?

  $I_{1}\omega_{1} =$$I_{2}\omega_{2}$
• Rotational dynamics is the study of objects rotating around a fixed axis
• What is rotational dynamics the study of?

  Motion of rotating objects
• Torque is the product of force and perpendicular distance from the axis.


  True
• Match the property with its description:

  Torque ↔️ Rotational force

  Moment of inertia ↔️ Resistance to rotational motion

  Units of torque ↔️ N·m

  Units of moment of inertia ↔️ kg·m²
• The formula for angular acceleration is α = Δω / Δt
• What is the formula for angular momentum?

  L = Iω
• Match the property with its unit:

  Angular acceleration ↔️ rad/s²

  Angular momentum ↔️ kg·m²/s

  Torque ↔️ N·m

  Moment of inertia ↔️ kg·m²
• Rotational kinetic energy is given by the formula K_r = 1/2 Iω²


  True
• What is the formula for linear kinetic energy?

  K_l = 1/2 mv²
• The principle of conservation of angular momentum is expressed as I₁ω₁ = I₂ω₂


  True
• What happens to an ice skater's angular velocity when they pull in their arms?

  Increases
• Match the property with its description:

  Angular Acceleration ↔️ Rate of change of angular velocity

  Angular Momentum ↔️ Amount of rotational motion
• The symbol ω in the rotational kinetic energy formula represents angular velocity.


  True
• Conservation of angular momentum states that the total angular momentum of a system remains constant if no external torque
• Ice skaters increase their spin speed by decreasing their moment of inertia.


  True
• What is the rotational analog of linear velocity?

  Angular velocity