Overview
This lecture explains the concepts of kinetic and potential energy, including their equations and when each applies, with examples involving translational and rotational motion.
Kinetic Energy Basics
- Kinetic energy is the energy of motion and exists when an object has both mass and velocity.
- The formula for translational kinetic energy is ( KE = \frac{1}{2}mv^2 ), where ( m ) is mass and ( v ) is velocity.
- Kinetic energy is measured in joules (J).
Rotational Kinetic Energy
- Objects that rotate have rotational kinetic energy, using angular velocity instead of linear velocity.
- The formula for rotational kinetic energy is ( KE_{rotational} = \frac{1}{2}I\omega^2 ), where ( I ) is moment of inertia (rotational inertia), and ( \omega ) is angular velocity.
- Both translational and rotational kinetic energy can exist simultaneously (e.g., a pitched baseball).
Potential Energy
- Potential energy requires more than one object; it's stored due to an object's position in a field (e.g., gravitational or electric).
- A single, isolated object cannot have potential energy; another object (like the Earth for gravity) must be present.
- Gravitational potential energy appears in systems like a pendulum and is converted to kinetic energy during motion.
- Electric potential energy similarly requires at least two charges or objects.
Example Calculations
- A 145 g baseball (0.145 kg) pitched at 41 m/s has ( KE = 0.5 \times 0.145 \times (41)^2 = 120 ) J.
- A spinning baseball with ( I = 0.047, kg, m^2 ) and ( \omega = 6.1, rad/s ) has ( KE_{rotational} = 0.5 \times 0.047 \times (6.1)^2 = 0.87 ) J (check the transcript: likely 8.7 or 87 J).
Key Terms & Definitions
- Kinetic Energy — Energy an object has due to its motion (( KE = \frac{1}{2}mv^2 )).
- Rotational Kinetic Energy — Energy due to an object's rotation (( KE_{rotational} = \frac{1}{2}I\omega^2 )).
- Potential Energy — Stored energy due to the position in a field, requiring interactions between at least two objects.
- Moment of Inertia (I) — A property representing rotational inertia depending on mass distribution.
- Angular Velocity (( \omega )) — The rate of change of angular position in radians per second.
Action Items / Next Steps
- Practice calculating kinetic and rotational kinetic energy for various objects.
- Review examples of potential energy in gravitational and electrical systems.
- Remember: a single object cannot have potential energy—identify the required system in problems.