11.1 Rotational dynamics

• Rotational motion refers to the motion of an object around a fixed axis
• 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
• 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 =$$\frac{v}{r}$, where $v$ is linear velocity and $r$ is the radius
• The relationship between torque, moment of inertia, and angular acceleration is $\tau =$$I\alpha$, where $I$ is the moment of inertia
• What does the moment of inertia (I) measure?

  Resistance to rotational motion
• Rotational kinetic energy is the energy an object possesses due to its rotational motion around a fixed axis
• What is the key difference between rotational and translational kinetic energy?

  Rotational KE depends on inertia
• Angular displacement is measured in radians
• Angular velocity is the rate of change of angular position
• Torque is the rotational force measured in Newton-meters
• The moment of inertia is a measure of an object's resistance to changes in its rotational motion
• Match the shape with its moment of inertia formula:

  Solid Disk ↔️ $I =$$\frac{1}{2}mr^{2}$

  Ring ↔️ $I =$$mr^{2}$
• The conservation of angular momentum states that the total angular momentum remains constant in a closed system if no external torque acts on it.


  True
• The mathematical expression for angular momentum is L = I\omega
• In rotational simple harmonic motion, the restoring torque is proportional to the angular displacement
• The equation for angular displacement in rotational SHM is \theta = A \sin(\omega t + \phi)
• The phase angle $\phi$ in rotational SHM determines the initial position
• What is the equation for rotational kinetic energy?

  KE_{rot} = \frac{1}{2}Iω^{2}</latex>
• 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