5.4 Rotational Inertia

• The farther the mass is from the axis of rotation, the greater the rotational inertia.


  True
• Linear inertia depends only on the object's mass.
• What is the effect of mass distribution on rotational inertia?

  Increases rotational inertia
• The distance of a particle from the axis of rotation is represented by the symbol 'r'.

  True
• Calculate the rotational inertia of a system with two particles: $m_{1} =$$2 kg$, $r_{1} =$$0.5 m$


  $0.5 \, kg \cdot m^{2}$
• Match the application of rotational inertia with its benefit:

  Flywheels ↔️ Smooth power delivery

  Spinning Tops ↔️ Enhanced stability

  Sports Balance ↔️ Controlled movements
• Rotational inertia is also known as the moment of inertia.

  True
• The more mass an object has, the greater its resistance to changes in rotational velocity
• The rotational inertia of a system with two particles is calculated to be 2.42 kg $\cdot$ m^{2}</latex>.
• The distance from the axis of rotation is represented by $r$ in rotational inertia calculations.


  True
• What is one application of flywheels in engines?

  Smooth power delivery
• The parallel axis theorem states that $I =$$I_{cm} +$$Md^{2}$, where $d$ is the distance between the two axes
• Why does the hollow ring have a higher rotational inertia than a solid disk with the same mass and radius?

  Mass is farther from axis
• Rotational inertia is analogous to mass in translational motion.
• Rank the factors affecting rotational inertia in order of their impact:

  1️⃣ Mass

  2️⃣ Mass Distribution
• A solid disk has less rotational inertia than a hollow ring of the same mass and radius
• The \sum symbol in the rotational inertia formula indicates the sum of all $mr^{2}$ values for each particle.
• Flywheels store rotational energy and smooth out power delivery
• How do flywheels store energy?

  By increasing rotational inertia
• What is rotational inertia analogous to in translational motion?

  Mass
• Why does a solid disk have less rotational inertia than a hollow ring of the same mass and radius?

  Mass is closer to axis
• Rotational inertia measures resistance to changes in rotational velocity
• What is the formula for calculating rotational inertia?

  $I =$$\sum mr^{2}$
• Spinning tops maintain stability due to rotational inertia resisting changes in their spin axis.


  True
• What is the formula for the parallel axis theorem?

  $I =$$I_{cm} +$$Md^{2}$
• Rotational inertia, often denoted as I, measures an object's resistance to changes in its rotational
• Rotational inertia depends only on the mass of the object.

  False
• What is the formula for calculating rotational inertia?

  $I =$$\sum mr^{2}$
• What is the formula for calculating rotational inertia?

  $I =$$\sum mr^{2}$
• Match the component with its symbol and description:

  Rotational Inertia ↔️ $I$, Measures resistance to changes in rotational velocity

  Mass of Particle ↔️ $m$, Amount of matter in each particle

  Distance from Axis ↔️ $r$, Distance of each particle from the rotation axis
• Gymnasts use rotational inertia to control their balance and movements.


  True
• Gyroscopes use rotational inertia to maintain orientation and stability
• Arrange the differences between rotational and linear inertia based on the table provided:

  1️⃣ Rotational inertia measures resistance to changes in rotational velocity.

  2️⃣ Linear inertia measures resistance to changes in linear velocity.

  3️⃣ Rotational inertia depends on mass and mass distribution.

  4️⃣ Linear inertia depends only on mass.

  5️⃣ The formula for rotational inertia is $I =$$\sum mr^{2}$.

  6️⃣ The formula for linear inertia is $F =$$ma$.
• The symbol 'I' represents rotational inertia in the formula $I =$$\sum mr^{2}$.


  True
• What does the symbol $m$ represent in the context of rotational inertia?


  Mass of particle
• In the rotational inertia formula, $m$ represents the mass of each particle
• How do flywheels store energy?

  By increasing rotational inertia
• Match the shape with its rotational inertia formula:

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

  Hollow Ring ↔️ $I =$$MR^{2}$

  Solid Sphere ↔️ $I =$$\frac{2}{5}MR^{2}$