Physical Quantities And Measurement Techniques

Physical Quantities & Measurement

• Physical quantities can be measured using appropriate instruments.
• Length is measured using rulers (mm), tape measures (cm), or trundle wheels (m).
• Volume of liquids is measured using measuring cylinders; irregular solid volume can be found by displacement.

Measuring Time & Multiple Readings

• Time intervals are measured using stop-clocks or stopwatches.
• Human reaction time (≈0.25 s) can cause errors, especially for short intervals.
• Taking multiple readings (e.g., time for 10 swings of a pendulum) and averaging reduces uncertainty.

Which instrument is most suitable for measuring the length of a running track (about 400 m)?

• Ruler
• Tape measure
• Trundle wheel
• Measuring cylinder

Scalars & Vectors

• Scalar quantities have only magnitude (e.g., mass, distance, speed).
• Vector quantities have both magnitude and direction (e.g., weight, displacement, velocity).

A quantity that has magnitude but no direction is called a ____. A quantity that has both magnitude and direction is called a ____.

Distance vs Displacement

• Distance is the total path length travelled; it is a scalar.
• Displacement is the straight-line distance from start to finish including direction; it is a vector.
• Example: walking 3 km east then 4 km north gives distance 7 km, displacement 5 km northeast.

A person walks 5 m east, then 5 m west. What is the total displacement?

• 10 m east
• 10 m west
• 0 m
• 5 m east

Speed vs Velocity

• Speed = distance / time; it is a scalar (no direction).
• Velocity = displacement / time; it is a vector (includes direction).
• An object can have constant speed but changing velocity if it changes direction (e.g., circular motion).

Which of these are vector quantities?

• Mass
• Weight
• Speed
• Acceleration

Common Scalars & Vectors

• Scalars: distance, speed, mass, energy, volume, density, temperature, power.
• Vectors: displacement, velocity, weight, force, acceleration, momentum.
• Corresponding pairs: distance/displacement, speed/velocity, mass/weight.

The ____ of an object can change even if its speed remains constant, because velocity includes ____.

Which of the following is a scalar quantity?

• Weight
• Displacement
• Energy
• Momentum

Measuring Length with a Ruler

• Rulers measure lengths to the nearest millimetre (mm).
• To measure the diameter of small objects, place several in a row and divide total length by the number.
• Example: four ball-bearings span 8 cm, so each diameter $= 8$ $cm / 4 = 2$ cm.

A student measures the length of 10 identical pins placed end-to-end as 12.5 cm. What is the diameter of one pin?

• 1.25 cm
• 12.5 cm
• 0.125 cm
• 125 cm

Measuring Time & Reaction Error

• Human reaction time is about 0.25 s, causing uncertainty in timing short events.
• To reduce error, measure the time for multiple oscillations (e.g., 10 swings) and divide by the number.
• A fiducial marker (e.g., a line at the equilibrium position) helps start/stop the timer consistently.

To measure the time period of a pendulum accurately, a student should:

• Measure the time for one swing only.
• Measure the time for 10 swings and divide by 10.
• Use a ruler instead of a stopwatch.
• Ignore reaction time.

Mass vs Weight

• Mass is a scalar: the amount of matter in an object; it does not change with location.
• Weight is a vector: the force due to gravity; it depends on gravitational field strength.
• Weight = mass × gravitational field strength (g).

An astronaut's ____ remains the same on the Moon, but their ____ is less because the Moon's gravity is weaker.

Which statement about scalars and vectors is correct?

• Speed is a vector because it has direction.
• Displacement is a scalar because it has magnitude only.
• Velocity is a vector because it has both magnitude and direction.
• Mass is a vector because it has direction.

Summary

• Use appropriate instruments for length, volume, and time measurements.
• Take multiple readings to reduce uncertainty.
• Distinguish between scalars (magnitude only) and vectors (magnitude and direction).
• Key pairs: distance/displacement, speed/velocity, mass/weight.