Rolling Motion Conservation of Energy Real Life Examples

📚 Quick Study Guide

• 🎢 Rolling Motion: Combination of translational (linear) and rotational motion.
• 🔄 Conservation of Energy: Total mechanical energy (kinetic + potential) remains constant in a closed system, assuming no non-conservative forces like friction.
• 📈 Potential Energy (PE): Energy due to an object's position or height. $PE = mgh$, where $m$ is mass, $g$ is the acceleration due to gravity, and $h$ is height.
• 💨 Translational Kinetic Energy (KE_trans): Energy due to an object's linear motion. $KE_{trans} = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is linear velocity.
• 💫 Rotational Kinetic Energy (KE_rot): Energy due to an object's rotation. $KE_{rot} = \frac{1}{2}I\omega^2$, where $I$ is the moment of inertia and $\omega$ is angular velocity.
• ⚖️ Total Kinetic Energy (KE_total): For rolling objects, $KE_{total} = KE_{trans} + KE_{rot}$.
• 🔗 Relationship between Linear and Angular Velocity: $v = r\omega$, where $r$ is the radius of the rolling object.

🧪 Practice Quiz

1. A solid sphere and a hollow sphere of the same mass and radius are released from the top of an inclined plane. Which one will reach the bottom first?
   1. The solid sphere
   2. The hollow sphere
   3. They will reach at the same time
   4. It depends on the angle of inclination
2. A bowling ball rolls down a bowling lane. What forms of kinetic energy does it possess?
   1. Translational only
   2. Rotational only
   3. Both translational and rotational
   4. Potential only
3. A hoop and a disk of the same mass and radius roll down an inclined plane without slipping. Which one has greater speed at the bottom?
   1. The hoop
   2. The disk
   3. They have the same speed
   4. It depends on the height of the incline
4. A marble rolls off a table. What happens to its total mechanical energy (assuming no air resistance)?
   1. It increases
   2. It decreases
   3. It remains constant
   4. It fluctuates
5. A bicycle wheel is rolling without slipping. What is the relationship between its linear velocity ($v$) and angular velocity ($\omega$)?
   1. $v = \omega$
   2. $v = r\omega$
   3. $\omega = rv$
   4. $v = \frac{\omega}{r}$
6. A solid cylinder rolls down an inclined plane. What percentage of its total kinetic energy at the bottom is rotational?
   1. 25%
   2. 33.3%
   3. 50%
   4. 66.7%
7. Which of the following real-world scenarios best demonstrates the conservation of energy with rolling motion?
   1. A car accelerating on a flat road
   2. A ball rolling up a hill, slowing down, and then rolling back down
   3. A block sliding down a frictionless ramp
   4. A spinning top slowing down due to friction