Topic 1 Motion, Forces, and Energy

1.1 Physical quantities and measurement techniques  

Measurement techniques: 

● Tools for measurement 

○ Rulers are used to measure length (precision ~1 mm) 

■ A micrometer screw gauge can be used to measure very small lengths (precision of 0.01mm) 

■ Vernier calipers measure internal/external diameters and depths 

(precision ~0.1 mm) 

○ Measuring cylinders are used to measure volume (read the bottom of the meniscus at eye level) 

○ Thermometers are used to measure temperature 

○ Clocks and digital timers are used to measure a variety of time intervals

■ Start and stop timing when the event begins and ends 

■ Used in experiments to measure duration, e.g., the period of oscillation of a pendulum 

■ Digital timers offer higher precision and reduce human error compared to manual stopwatches 

● By measuring multiples, you can get an average value for a small distance and for a short interval of time (e.g., use total time for 10 swings of a pendulum) 

Physical quantities: 

● A scalar quantity has magnitude (size) only 

○ Eg: distance, speed, time, mass, energy, and temperature 

● A vector quantity has magnitude and direction 

○ Eg: force, weight, velocity, acceleration, momentum, electric field strength, and gravitational field strength 

● How to determine the resultant of two vectors (forces or velocities) at right angles?

○ Calculation 

■ Use the Pythagorean theorem: 

Resultant = R = √(A² + B²)

■ Find the direction using: 

θ = tan⁻¹(opposite / adjacent)

θ = sin⁻¹(opposite / hypotenuse)

θ = cos⁻¹(adjacent / hypotenuse)

A / B or B / A

where A and B are the magnitudes of the two vectors. 

○ Graphically 

■ Vectors are drawn to scale as arrows at right angles (length is their magnitude) so that a diagonal from their origin gives us the resultant.

■ Use the head-to-tail method -> Draw the resultant from the tail of the first to the head of the second.

■ Measure the length and angle of the resultant using a ruler and protractor.

Written by: Charis Liao

Edited by: Yassein Abdoun