Momentum (Grade 12 NSC Matric Physical Sciences): Revision Notes

Momentum

What is momentum?

Momentum is a fundamental concept in physics that describes the motion of objects. It is closely related to forces and represents a property that applies to all moving objects - essentially, it is mass in motion. When something has mass and is moving, it possesses momentum.

Definition and formula

Momentum is defined as a vector quantity that depends on both the mass and velocity of an object.

The mathematical relationship is expressed as:

$p = mv$

Where:

• $p$ = momentum (measured in $kg \cdot m \cdot s^{-1}$)
• $m$ = mass (measured in $kg$)
• $v$ = velocity (measured in $m \cdot s^{-1}$)

From this formula, we can see that momentum is directly proportional to both mass and velocity. This means:

• A small car travelling at the same velocity as a big truck will have smaller momentum than the truck
• If mass stays constant, the greater the velocity, the greater the momentum
• If velocity stays constant, the greater the mass, the greater the momentum

Vector nature of momentum

Since momentum equals mass multiplied by velocity, and mass is a scalar while velocity is a vector, momentum is always a vector quantity. This means momentum has both magnitude and direction.

For example, a car travelling at $120km \cdot hr^{-1}$ will have larger momentum than the same car travelling at $60km \cdot hr^{-1}$. Similarly, a heavy motorcycle travelling slowly can have the same momentum as a light car travelling relatively fast.

Worked examples

Change in momentum

When objects collide with other objects or barriers, their velocity often changes, which means their momentum changes too. Understanding how momentum changes is crucial for analysing collisions and interactions.

Case 1: Object bouncing off a wall

Consider a ball moving towards a wall with initial momentum $p_i$ pointing right.

After bouncing, the ball moves away from the wall with final momentum $p_f$ pointing left.

The change in momentum is the vector difference between final and initial momentum:

Case 2: Object stops

In some scenarios, an object may come to a complete stop (like a tennis ball hitting a net). When this happens:

• Initial momentum: $p_i$ (in original direction)
• Final momentum: $p_f = 0$
• Change in momentum: $\Delta p = 0 - p_i = -p_i$

Case 3: Object continues more slowly

Sometimes an object continues in the same direction but with reduced speed (like a ball hitting a glass window and going through, or sliding on a rough surface).

Case 4: Object gets a boost

When an object interacts with something that increases its velocity without changing direction (like a squash ball bouncing off a back wall after being hit by a racquet):

• Both momenta point in the same direction
• Final momentum has greater magnitude than initial momentum
• Change in momentum points in the same direction as motion

Case 5: Vertical bounce

The same principles apply to vertical motion. When a basketball bounces off the floor:

• Initial momentum points downward
• Final momentum points upward
• Change in momentum is large due to the direction change

Exam tips