11.1 Rotational dynamics

• Angular velocity is measured in units of radians per second
• Angular displacement is related to linear displacement by the formula $\theta =$$\frac{s}{r}$, where $s$ is linear displacement and $r$ is the radius
• What is torque defined as in rotational dynamics?

  Rotational force
• What does the moment of inertia measure in rotational dynamics?

  Resistance to rotation
• The greater the moment of inertia of an object, the less torque is required to produce the same angular acceleration.

  False
• What is the formula for rotational kinetic energy (KE_rot)?

  $KE_{rot} =$$\frac{1}{2}I\omega^{2}$
• Match the rotational motion quantity with its unit:

  Angular Displacement (θ) ↔️ Radians (rad)

  Angular Velocity (ω) ↔️ Radians per second (rad/s)

  Angular Acceleration (α) ↔️ Radians per second squared (rad/s²)
• Linear velocity is equal to angular velocity multiplied by the radius.


  True
• Angular acceleration is measured in radians per second squared.


  True
• A higher moment of inertia results in lower angular acceleration for the same torque.


  True
• The moment of inertia depends only on the object's mass.

  False
• Rotational kinetic energy is calculated using the formula KE_{rot} = \frac{1}{2}I\omega^{2}</latex>, where $I$ is the moment of inertia
• Angular momentum is defined as the product of moment of inertia and angular velocity
• Linear momentum is conserved when there is no external force acting on the system

  True
• Angular displacement in rotational SHM varies sinusoidally with time


  True
• What does $A$ represent in the equation for angular displacement in rotational SHM?


  Amplitude
• How is rotational simple harmonic motion analogous to linear simple harmonic motion?

  Uses angular quantities
• The total angular momentum of a closed system remains constant according to the conservation of angular momentum
• Rotational motion refers to the motion of an object around a fixed axis
• Angular velocity is the rate of change of angular position
• Angular velocity is equal to linear velocity divided by the radius.


  True
• The relationship between torque, moment of inertia, and angular acceleration is given by $\tau =$$I\alpha$.


  True
• A higher moment of inertia requires more torque to produce the same angular acceleration.


  True
• Match the rotational quantity with its definition or relation to moment of inertia:

  Torque (τ) ↔️ Rotational force

  Angular Acceleration (α) ↔️ Rate of change of angular velocity

  Angular Velocity (ω) ↔️ Rate of change of angular position
• The rotational kinetic energy formula uses angular velocity, while the translational kinetic energy formula uses linear velocity.


  True
• What is the definition of angular displacement (θ)?

  Change in angular position
• What is the definition of angular displacement?

  Change in angular position
• What is the relationship between linear displacement and angular displacement?

  Linear displacement = Angular displacement × Radius
• What is the relation between torque, moment of inertia, and angular acceleration?

  $\tau =$$I\alpha$
• What is the moment of inertia formula for a solid disk?

  $I =$$\frac{1}{2}mr^{2}$
• What is the rotational kinetic energy of a flywheel with a moment of inertia of 4 \, \text{kg·m²} spinning at $5 \, \text{rad / s}$?


  $50 \, \text{J}$
• What does the conservation of angular momentum state about a closed system without external torque?

  Angular momentum remains constant
• What happens to the moment of inertia and angular velocity of an ice skater when they pull their arms closer to their body?

  Inertia decreases, velocity increases
• Match the quantity with its relationship in rotational SHM:

  Angular Velocity (ω) ↔️ Cosinusoidal with time

  Angular Acceleration (α) ↔️ Proportional to -θ
• Arrange the equations for rotational SHM in the correct order:

  1️⃣ $\theta =$$A \sin(\omega t + \phi)$

  2️⃣ $\omega =$$A\omega \cos(\omega t + \phi)$

  3️⃣ $\alpha =$$- A\omega^{2} \sin(\omega t + \phi)$
• Torque is defined as the rotational force that causes an object to rotate


  True
• What is one engineering application of flywheels?

  Stabilizing machines
• Angular displacement is measured in units of radians
• Linear displacement is equal to angular displacement multiplied by the radius.

  True
• Angular velocity is related to linear velocity by the formula $\omega =$$\frac{v}{r}$, where $v$ is linear velocity and $r$ is the radius