11.1 Rotational dynamics

• Angular displacement is measured in radians.

  True
• What is the formula for torque when the force is perpendicular to the lever arm?

  $\tau =$$rF$
• What is rotational kinetic energy the energy of?

  Rotating object
• What are the two key factors that rotational kinetic energy depends on?

  Moment of inertia and angular velocity
• Match the feature with its type of dynamics:

  Movement ↔️ Rotation around an axis

  Force ↔️ Torque

  Effect ↔️ Angular acceleration
• What is moment of inertia analogous to in linear motion?

  Mass
• Torque is measured in Newton-meters (N·m).


  True
• Torque is a rotational force that causes an object to rotate about an axis
• Torque is measured in Newton-meters
• The moment of inertia measures an object's resistance to changes in rotational motion.

  True
• Match the type of energy with its key factors:

  Rotational Kinetic Energy ↔️ Moment of inertia, Angular velocity

  Linear Kinetic Energy ↔️ Mass, Linear velocity
• The formula for angular momentum is L = I\omega</latex>.


  True
• The conservation of angular momentum states that the total angular momentum of a closed system remains constant unless acted upon by an external torque.


  True
• Match the type of momentum with its conservation principle:

  Linear Momentum ↔️ Total linear momentum remains constant unless acted upon by an external force

  Angular Momentum ↔️ Total angular momentum remains constant unless acted upon by an external torque
• What is the symbol for linear momentum?

  $p$
• What is the formula for linear momentum?

  $p =$$mv$
• What type of motion is described by rotational simple harmonic motion?

  Rotational motion around an axis
• The period of rotational simple harmonic motion is given by $T =$$\frac{2\pi}{\omega_{0}}$, where $\omega_{0}$ is the angular frequency
• Torque is measured in Newton-meters.


  True
• Arrange the concepts of rotational dynamics in a logical sequence:

  1️⃣ Define rotational dynamics

  2️⃣ Angular displacement and angular velocity

  3️⃣ Moment of inertia

  4️⃣ Torque

  5️⃣ Rotational kinetic energy
• The formula for rotational kinetic energy is $\frac{1}{2}I\omega^{2}$
• What is rotational dynamics the study of?

  Forces and torques causing rotation
• Angular velocity is the rate of change of angular displacement with time.


  True
• What is the formula for torque when the force is applied perpendicular to the lever arm?

  $\tau =$$rF$
• What does torque cause in rotational motion?

  Rotation about an axis
• What is the formula for torque when the force is applied perpendicular to the lever arm?

  $\tau =$$rF$
• Rotational kinetic energy depends on the object's moment of inertia and angular velocity
• The formula for linear kinetic energy is $KE_{lin} =$$\frac{1}{2}mv^{2}$, where $m$ is the mass and $v$ is the linear velocity
• Angular momentum is the rotational equivalent of linear momentum
• Match the type of momentum with its key components:

  Linear Momentum ↔️ Mass, Linear velocity

  Angular Momentum ↔️ Moment of inertia, Angular velocity
• A figure skater pulling their arms in is an example of the conservation of angular momentum.


  True
• If the moment of inertia of an object decreases and no external torque is applied, its angular velocity must increase.


  True
• Match the dependent variables of linear and angular momentum:

  Linear momentum ↔️ Mass and Linear Velocity

  Angular momentum ↔️ Moment of Inertia and Angular Velocity
• Angular momentum is a measure of rotational motion
• What is the formula for angular displacement in rotational simple harmonic motion?

  \theta = \theta_{0} \cos(\omega t)</latex>
• What is the formula for angular velocity?

  $\omega =$$\frac{d\theta}{dt}$
• The formula for rotational kinetic energy is $KE_{rot} =$$\frac{1}{2}I\omega^{2}$.


  True
• The moment of inertia measures an object's resistance to changes in rotational motion.


  True
• Rotational kinetic energy has parallels with linear kinetic energy.


  True
• What is the unit of angular displacement?

  Radians (rad)