Physical quantities and measurements

In physics, measurement is key to understanding and describing the natural world. This section covers how to measure different quantities, the distinction between scalar and vector quantities, and how to determine the result of vector interactions.

Measuring length, volume and time

Accurate measurements are fundamental in physics. Here are some methods and tools used to measure length, volume, and time:

(a) Length and Volume:

• Rulers are commonly used to measure length. A ruler has a calibrated scale in millimeters and centimeters, which allows precise measurement of straight-line distances.

• Measuring Cylinders are used to determine the volume of a liquid. You read the level of the liquid from the scale on the side of the cylinder. For better accuracy, read the liquid's meniscus at eye level.

(b) Time Measurement:

• Various tools can be used to measure time intervals:

  • Clocks provide approximate time intervals, suitable for events that last minutes or longer.

  • Digital Timers are used for shorter and more precise intervals, like measuring the time taken for a simple reaction or event.

(c) Average Measurements:

• For small distances or short time intervals, it is often helpful to take multiple measurements and calculate an average value. This helps reduce random errors.

• For example, when measuring the period of oscillation of a pendulum, measure the time taken for several oscillations and divide by the number of oscillations to get the average period.

Scalar and vector quantities

In physics, it is important to differentiate between scalar and vector quantities:

(a) Scalars:

• A scalar quantity has only magnitude (size) but no direction. Scalars tell us how much of something there is, but not where it is heading.

• Examples of scalar quantities include:

  • Distance: The total length of the path traveled, regardless of direction.

  • Speed: How fast an object is moving, without considering direction.

  • Time: How long an event lasts.

  • Mass: The amount of matter in an object.

  • Energy: The ability to do work.

  • Temperature: A measure of thermal energy.

(b) Vectors:

• A vector quantity has both magnitude and direction. Vectors describe not just how much, but also where.

• Examples of vector quantities include:

  • Force: A push or pull, with a specific direction.

  • Weight: The force of gravity acting on an object, directed towards the center of the Earth.

  • Velocity: Speed in a particular direction.

  • Acceleration: The rate of change of velocity, including its direction.

  • Momentum: The product of an object's mass and velocity, including its direction.

  • Electric Field Strength: The force experienced by a positive test charge in an electric field.

  • Gravitational Field Strength: The force per unit mass experienced in a gravitational field.

Determining the resultant of two vectors

Vectors can interact, and their combined effect is represented by the resultant vector. To find the resultant of two vectors, especially when they are at right angles, you can use either calculation or a graphical method:

(a) Calculation Method:

• If two vectors are at right angles to each other, you can use the Pythagorean theorem to calculate the resultant vector.

• For example, if you have a force of 3 N acting east and another force of 4 N acting north, the magnitude of the resultant force is: