1. **Linear Momentum:**
- **Definition:** Linear momentum is the product of an object's mass and its velocity. It represents the quantity of motion in a straight line.
- **Formula:** Linear momentum = (mass) (velocity), typically denoted as
p = mv .
- **SI Unit:** Kilogram meter per second (kg m/s).
- **CGS Unit:** Gram centimeter per second (g cm/s).
- **Dimension:** \([M] \cdot [L] \cdot [T]^{-1}\) (Mass × Length × Time\(^{-1}\)).
- **Example:** A car moving with a mass of 1000 kg at a velocity of 20 m/s has a linear momentum of 1000 * 20 = 20000 kg m.
2. **Angular Momentum:**
- **Definition:** Angular momentum is a measure of the rotational motion of an object around an axis. It depends on both the object's rotational inertia (moment of inertia) and its angular velocity.
- **Formula:** \( \text{Angular momentum} = \text{moment of inertia} \times \text{angular velocity} \), typically denoted as \( L = I\omega \).
- **SI Unit:** Kilogram meter squared per second (kg m\(^2\)/s).
- **CGS Unit:** Gram centimeter squared per second (g cm\(^2\)/s).
- **Dimension:** \([M] \cdot [L]^2 \cdot [T]^{-1}\) (Mass × Length\(^2\) × Time\(^{-1}\)).
- **Example:** A rotating bicycle wheel with a moment of inertia of 2 kg m\(^2\) and an angular velocity of 10 rad/s has an angular momentum of \(2 \times 10 = 20 \, \text{kg m}^2/\text{s}\).
In summary, linear momentum relates to straight-line motion, while angular momentum relates to rotational motion. They have different formulas, units, and dimensions reflecting their distinct characteristics.
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