6.4 Rolling Motion

• In rolling motion, translational speed refers to the speed at which the center of mass moves
• Match the type of kinetic energy with its description and formula:

  Translational Kinetic Energy ↔️ Energy due to linear movement; $KE_{trans} =$$\frac{1}{2}mv^{2}$

  Rotational Kinetic Energy ↔️ Energy due to spinning around an axis; $KE_{rot} =$$\frac{1}{2}I\omega^{2}$
• Pure rolling occurs when the contact point between the object and the surface has zero relative velocity.


  True
• What is the contact point velocity in rolling with slipping?

  Non-zero
• The angular speed in rotational kinetic energy is denoted by \omega
• What type of friction is involved in rolling with slipping?

  Kinetic friction
• Rolling with slipping uses static friction.

  False
• The formula for translational kinetic energy is $KE_{trans}$ = $\frac{1}{2}mv^{2}$.
• The total momentum in a rolling system is the sum of translational and rotational momentum.


  True
• Match the momentum type with its formula:

  Translational ↔️ $p_{trans} =$$mv$

  Rotational ↔️ $L =$$I\omega$

  Total ↔️ $\vec{p}_{total} =$$\vec{p}_{trans} +$$\vec{L}$
• The conservation equation in rolling motion includes translational kinetic energy, rotational kinetic energy, and gravitational potential energy.

  True
• What is the final velocity of a solid sphere rolling down an inclined plane of height h?

  v = \sqrt{\frac{10gh}{7}}</latex>
• Gravitational potential energy depends on the height above a reference point.

  True
• What is the equation for conservation of energy in rolling motion?

  $KE_{trans} +$$KE_{rot} +$$PE_{g} =$$constant$
• What two types of motion combine to form rolling motion?

  Translation and rotation
• In pure rolling, the contact point between the object and the surface has zero relative velocity.


  True
• What is the formula for total kinetic energy in rolling motion?

  $KE_{total} =$$\frac{1}{2}mv^{2} +$$\frac{1}{2}I\omega^{2}$
• Match the momentum type with its description:

  Translational Momentum ↔️ Linear motion of center of mass

  Rotational Momentum ↔️ Rotation around axis
• What is the formula for rotational kinetic energy?

  $KE_{rot} =$$\frac{1}{2}I\omega^{2}$
• The conservation of energy equation for rolling motion is KE_{trans} + KE_{rot} + PE_{g} = constant</latex>
• A solid sphere rolls down an inclined plane of height $h$. What is its velocity at the bottom?


  $v =$$\sqrt{\frac{10gh}{7}}$
• A solid sphere of mass 5 kg and radius 0.2 m rolls down an inclined plane of height 3 m. Calculate its linear speed at the bottom.

  $v \approx 6.48 m / s$
• What type of friction is involved in rolling with slipping?

  Kinetic friction
• Match the type of rolling motion with its characteristics:

  Pure Rolling ↔️ Zero relative velocity, static friction

  Rolling with Slipping ↔️ Non-zero relative velocity, kinetic friction
• What is rolling motion a combination of?

  Translation and rotation
• What are the two main types of rolling motion?

  Pure rolling and slipping
• In pure rolling, the friction involved is static friction
• What is the formula for total kinetic energy in rolling motion?

  KE_{total} = \frac{1}{2}mv^{2} + \frac{1}{2}I\omega^{2}</latex>
• What does $I$ represent in the formula for rotational kinetic energy?


  Moment of inertia
• Rolling motion combines translation and rotation around an axis.

  True
• Pure rolling occurs when the contact point has non-zero relative velocity.

  False
• In pure rolling, static friction maintains grip
• Order the steps to describe the key differences between pure rolling and rolling with slipping:

  1️⃣ Pure rolling has zero relative velocity at the contact point.

  2️⃣ Rolling with slipping has non-zero relative velocity at the contact point.

  3️⃣ Pure rolling uses static friction to maintain grip.

  4️⃣ Rolling with slipping uses kinetic friction due to sliding.
• What is the contact point velocity in pure rolling motion?

  Zero
• What type of kinetic energy is due to an object's movement from one location to another?

  Translational
• What is the rotational kinetic energy formula?

  $KE_{rot} =$$\frac{1}{2}I\omega^{2}$
• The total kinetic energy in rolling motion is the sum of translational and rotational kinetic energy.
• What is conserved in a rolling system in the absence of external non-conservative forces?

  Total momentum
• Conservation of energy in rolling motion states that the total mechanical energy remains constant if no external non-conservative forces are present.
• What does the conservation of energy in rolling motion state?

  Total mechanical energy remains constant