Motion, Forces, and Energy
Physical Quantities and Measurement Techniques
Making Measurements
Importance: Accurate numerical measurements are crucial in physics for precise comparisons and
reliable scientific progress.
Instruments:
Rulers and tape measures: Used for measuring length.
Stopwatches and digital timers: Used for measuring time intervals.
Measuring cylinders: Used for measuring volume.
Accuracy:
Length: Place the ruler along the object and read the positions of the beginning and end. The
length is the difference. Ensure the line of sight is perpendicular to the ruler to avoid parallax
error.
Volume: Stand the measuring cylinder on a level table. Read the volume at the bottom of the
meniscus (the curved surface of a liquid). Ensure your eye is level with the liquid surface.
Time: Hand-operated stopwatches have a reaction time (around 0.2 s) that limits accuracy. For
critical measurements, automatic starting/stopping (e.g., light beams) is used.
Improving Accuracy:
Take multiple readings and calculate the average.
For short time intervals (like the period of oscillation of a pendulum), time multiple oscillations
and divide the total time by the number of oscillations.
Scalar and Vector Quantities
Scalar Quantity: Has magnitude (size) only.
Examples: Distance, speed, time, mass, energy, temperature, volume.
Addition: Similar scalar quantities are added by simply adding their values.
, Vector Quantity: Has both magnitude and direction.
Examples: Force, weight, velocity, acceleration, momentum, electric field strength, gravitational
field strength.
Representation: Can be shown by an arrow where length represents magnitude and arrowhead
points in the direction.
Addition: The total vector is called the resultant vector.
Same Direction: Magnitudes are added.
Opposite Directions: Magnitudes are subtracted.
At Right Angles: The resultant can be found using scale drawings (trigonometry) or
calculations (Pythagorean theorem and trigonometry).
Magnitude: F = 302 + 402 = 50 N
40 ∘
Direction: tan θ = 30 = 1.333 ⟹ θ = 53
Motion
Calculating Speed
Definition: Speed is the distance travelled per unit time.
Equation for Constant Speed:
s
v=
t
where:
v = speed in m/s
s = distance in m
t = time in s
Equation for Average Speed:
total distance travelled
average speed =
total time taken
Worked Example: A car travels 500 m in 20 s.
500 m
v= = 25 m/s
20 s
Speed and Velocity
Velocity: Speed in a given direction.
Sign Convention: A negative velocity indicates movement in the opposite direction to the chosen
positive direction.
Physical Quantities and Measurement Techniques
Making Measurements
Importance: Accurate numerical measurements are crucial in physics for precise comparisons and
reliable scientific progress.
Instruments:
Rulers and tape measures: Used for measuring length.
Stopwatches and digital timers: Used for measuring time intervals.
Measuring cylinders: Used for measuring volume.
Accuracy:
Length: Place the ruler along the object and read the positions of the beginning and end. The
length is the difference. Ensure the line of sight is perpendicular to the ruler to avoid parallax
error.
Volume: Stand the measuring cylinder on a level table. Read the volume at the bottom of the
meniscus (the curved surface of a liquid). Ensure your eye is level with the liquid surface.
Time: Hand-operated stopwatches have a reaction time (around 0.2 s) that limits accuracy. For
critical measurements, automatic starting/stopping (e.g., light beams) is used.
Improving Accuracy:
Take multiple readings and calculate the average.
For short time intervals (like the period of oscillation of a pendulum), time multiple oscillations
and divide the total time by the number of oscillations.
Scalar and Vector Quantities
Scalar Quantity: Has magnitude (size) only.
Examples: Distance, speed, time, mass, energy, temperature, volume.
Addition: Similar scalar quantities are added by simply adding their values.
, Vector Quantity: Has both magnitude and direction.
Examples: Force, weight, velocity, acceleration, momentum, electric field strength, gravitational
field strength.
Representation: Can be shown by an arrow where length represents magnitude and arrowhead
points in the direction.
Addition: The total vector is called the resultant vector.
Same Direction: Magnitudes are added.
Opposite Directions: Magnitudes are subtracted.
At Right Angles: The resultant can be found using scale drawings (trigonometry) or
calculations (Pythagorean theorem and trigonometry).
Magnitude: F = 302 + 402 = 50 N
40 ∘
Direction: tan θ = 30 = 1.333 ⟹ θ = 53
Motion
Calculating Speed
Definition: Speed is the distance travelled per unit time.
Equation for Constant Speed:
s
v=
t
where:
v = speed in m/s
s = distance in m
t = time in s
Equation for Average Speed:
total distance travelled
average speed =
total time taken
Worked Example: A car travels 500 m in 20 s.
500 m
v= = 25 m/s
20 s
Speed and Velocity
Velocity: Speed in a given direction.
Sign Convention: A negative velocity indicates movement in the opposite direction to the chosen
positive direction.
