Motion and forces Revision Notes

Scalar Quantities

A scalar quantity is fully described by its magnitude (size) alone. It does not require a direction. Common examples include: distance, speed, mass, energy, power, time, and temperature. For instance, when you say a car travels for 30 minutes, the '30 minutes' completely defines the time interval.

Vector Quantities

A vector quantity requires both magnitude and direction for its complete description. Without specifying a direction, the quantity is not fully understood. Common examples include: displacement, velocity, acceleration, force, momentum, and weight. For example, a displacement of '5 km north' indicates both the distance and the specific direction of travel from a starting point.

Key Difference and Representation

The crucial difference lies in the presence or absence of direction. Scalars add arithmetically (e.g., 2 kg + 3 kg = 5 kg). Vectors, however, often require graphical representation (like arrows where length represents magnitude and arrowhead shows direction) or vector mathematics for addition and subtraction, as their directions must be taken into account. For instance, two forces of 5 N each can result in anything from 0 N to 10 N depending on their directions relative to each other.

Scalar Quantities: Magnitude Only

Scalar quantities are physical measurements that are completely characterised by a magnitude, which is a numerical value along with its unit. They do not have any associated direction. Examples include: distance (e.g., 5 km), speed (e.g., 60 km/h), mass (e.g., 70 kg), energy (e.g., 100 J), and temperature (e.g., 20 °C). When working with scalars, they can be added or subtracted using simple arithmetic operations.

Vector Quantities: Magnitude and Direction

Vector quantities are physical measurements that possess both a magnitude and a specific direction. Both aspects are crucial for their complete description. Examples include: displacement (e.g., 5 km North), velocity (e.g., 60 km/h East), acceleration (e.g., 9.8 m/s² downwards), force (e.g., 10 N to the left), weight (e.g., 700 N downwards), and momentum (e.g., 100 kg m/s forwards). When adding or subtracting vectors, their directions must be taken into account, often using graphical methods or trigonometry.

Key Examples to Remember

It's important to be able to identify common quantities as either scalar or vector. Here's a quick reference:

• Scalar: Distance, Speed, Mass, Energy (including kinetic and potential), Time, Temperature, Density, Work.
• Vector: Displacement, Velocity, Acceleration, Force, Weight, Momentum, Impulse, Electric field.

Defining Speed

Speed is a scalar quantity that measures how quickly an object is moving. It quantifies the rate at which distance is covered, without reference to the direction of travel. Its magnitude is calculated as distance divided by time. Common units include metres per second (m/s) and kilometres per hour (km/h).

Defining Velocity

Velocity is a vector quantity that measures the rate of change of an object's displacement. It includes both the magnitude of movement (speed) and the specific direction of that movement. For example, '50 m/s east' is a velocity, whereas '50 m/s' alone is a speed. A change in direction, even if speed remains constant, signifies a change in velocity.

Key Difference: Direction

The fundamental difference between speed and velocity is that velocity includes a specified direction, while speed does not. This is why velocity is considered a vector quantity and speed is a scalar quantity. Understanding this distinction is essential for describing motion accurately and solving problems in kinematics.

Definition of Momentum

Momentum is a measure of the 'quantity of motion' an object has. It depends on an object's mass and its velocity. The greater the mass or the greater the velocity, the greater the momentum. It is a vector quantity, so direction is important.

Momentum Equation and Units

Momentum (p) is calculated by multiplying an object's mass (m) by its velocity (v). The equation is: p = m × v. The standard unit for mass is kilograms (kg), and for velocity is metres per second (m/s). Therefore, the unit for momentum is kilogram metre per second (kg m/s).

Calculating Momentum

To calculate momentum, ensure all values are in their standard SI units: mass in kg and velocity in m/s. If units are provided differently (e.g., mass in grams or velocity in km/h), they must first be converted before applying the formula p = m × v. For example, 1 kg = 1000 g, and 1 m/s = 3.6 km/h (or 1 km/h = 1000/3600 m/s).