IAL Edexcel Physics – Topic 5: Further Mechanics

5A: Further Momentum

Momentum is a vector quantity. In "Further Mechanics," we extend the Principle of Conservation of Momentum to 2D systems and analyze the relationship between force and time (Impulse).

1. Momentum and Newton's Second Law

Newton’s Second Law is more fundamentally defined as the rate of change of momentum:

$$F=\frac{\Delta p}{\Delta t}=\frac{m(v-u)}{\Delta t}$$

2. Impulse

Impulse is the change in momentum, equivalent to the area under a Force-Time graph.

• Unit: N s or kg m s⁻¹
• Formula: Impulse = $F\Delta t$

3. Collisions in Two Dimensions

In 2D collisions, momentum must be conserved in two mutually perpendicular directions (usually horizontal x and vertical y).

Key tip: Resolve initial and final velocities into v cos(θ) and v sin(θ) components before applying conservation laws.

4. Elastic and Inelastic Collisions

• Elastic: Momentum and Kinetic Energy are both conserved.
• Inelastic: Momentum is conserved, but Kinetic Energy is not (converted to heat/sound).

Kinetic Energy Formula:

$$E_k=\frac{p^2}{2m}$$

5B: Circular Motion

Circular motion occurs when a net force acts perpendicular to the velocity of an object, changing its direction but not its speed.

1. Angular Velocity (ω)

Angular velocity is the rate of change of angle (in radians).

$$\omega =\frac{v}{r}=2\pi f=\frac{2\pi }{T}$$

2. Centripetal Acceleration

Even at constant speed, an object in a circle is accelerating because its direction is constantly changing. This acceleration is always directed toward the center.

$$a=\frac{v^2}{r}={\omega }^{2}r$$

3. Centripetal Force

The centripetal force is not a new type of force; it is the name given to the resultant force (tension, friction, gravity, etc.) acting toward the center.

$$F=\frac{m{v}^2}{r}=m{\omega }^{2}r$$

4. Vertical Circular Motion

In a vertical circle (like a rollercoaster loop), the required centripetal force is provided by the combination of the Normal Contact Force (N) and Weight (mg).

• At the top: $N+mg=\frac{m{v}^2}{r}$
• At the bottom: $N-mg=\frac{m{v}^2}{r}$

Summary: Always identify the source of the centripetal force in your free-body diagrams!