momentum

. Definition of Momentum

  • Momentum (p) is the quantity of motion of an object

  • Formula:
    p = mv

    • m = mass (kg)

    • v = velocity (m/s)

  • Unit: kg·m/s

  • Momentum is a vector quantity (has magnitude and direction)

  • Direction of momentum = direction of velocity

  • If an object is at rest, its momentum is zero

II. Types of Momentum

  • Linear momentum: motion in a straight line

  • Angular momentum: motion in a circular path

  • This lesson focuses only on linear momentum

III. How Mass and Velocity Affect Momentum

  • Momentum is directly proportional to:

    • Mass

    • Velocity

  • Increasing mass or velocity increases momentum by the same factor

Comparisons

  • Same velocity → heavier object has more momentum

  • Same mass → faster object has more momentum

Examples

  • Motorcycle vs bicycle at same speed → motorcycle has more momentum

  • Two identical motorcycles → faster one has more momentum

IV. Proportionality Examples

  • 10 kg cart at 4 m/s →
    p = 40 kg·m/s

  • Double mass (20 kg, same speed) →
    p = 80 kg·m/s

  • Double velocity (10 kg, 8 m/s) →
    p = 80 kg·m/s

V. Historical Background

  • Galileo Galilei

    • First explained momentum

    • Identified weight and velocity as key factors

  • Isaac Newton

    • Defined inertia

    • Inertia = resistance to changes in motion

    • Inertia is proportional to mass

    • Objects with more inertia have more momentum when moving

VI. Momentum vs. Kinetic Energy

Key Differences

Momentum

Kinetic Energy

Vector quantity

Scalar quantity

Depends on direction

No direction

p = mv

KE = ½mv²

Proportional to velocity

Proportional to velocity²

Velocity Effect

  • Double velocity:

    • Momentum doubles

    • Kinetic energy quadruples

VII. Forms and Conservation

  • Energy

    • Exists in many forms

    • Can be converted from one form to another

  • Momentum

    • Cannot change form

    • Can only be transferred between objects

VIII. Law of Conservation of Momentum

  • In an isolated system:

    • Total momentum before interaction = total momentum after interaction

  • Applies to:

    • Collisions

    • Pushes

    • Any force interaction

Connection to Newton’s Third Law

  • Forces are equal and opposite

  • Lighter object moves faster

  • Heavier object moves slower

  • Total momentum remains constant

IX. Momentum and Energy Relationship

  • Momentum equation:
    p = mv

  • Kinetic energy equation:
    KE = ½mv²

  • By substitution:

    • Higher momentum → higher kinetic energy

  • They are related but not the same

X. Solving Momentum Problems

Steps

  1. Find total mass

  2. Convert velocity to m/s

  3. Use p = mv

  4. Include direction

Example

  • Girl: 25 kg

  • Bike: 5 kg

  • Total mass = 30 kg

  • Velocity = 5.5 m/s east

p=30×5.5=165 kg\cdotpm/s eastp = 30 \times 5.5 = 165 \text{ kg·m/s east}p=30×5.5=165 kg\cdotpm/s east

XI. Key Takeaways

  • Momentum depends on mass and velocity

  • It is a vector

  • Conserved in isolated systems

  • Closely related to inertia and Newton’s laws

  • Different from kinetic energy but connected to it