Measurement, Motion and Forces: notes

Measuring and Units

• Physical quantity: something we can measure with a number and a unit, such as length, mass or time.
• SI units: the standard units used in science. Length is in metres (m), mass in kilograms (kg), time in seconds (s), temperature in kelvin (K) or degrees Celsius (°C).
• Length: measured with a metre rule or vernier calipers. Read the scale at eye level to avoid parallax error.
• Mass: measured with a beam balance or electronic balance. Mass is the amount of matter in an object.
• Volume: a measuring cylinder for liquids. Read the bottom of the curved surface (meniscus) at eye level.
• Temperature: measured with a thermometer. Time is measured with a stopwatch or clock.

Scalars, Vectors and Motion

• Scalar: a quantity with size only, such as distance, speed, mass or time.
• Vector: a quantity with size and direction, such as displacement, velocity, acceleration or force.
• Speed: distance moved per unit time. Speed = distance ÷ time.
• Velocity: speed in a given direction.
• Acceleration: change in velocity per unit time. Acceleration = (final velocity − initial velocity) ÷ time.
• Distance-time graph: a steeper line means a higher speed. A flat line means the object is at rest.
• Speed-time graph: the gradient gives acceleration; the area under the line gives distance travelled.

Worked calculation: A car travels 240 m in 16 s. Speed = 240 ÷ 16 = 15 m/s.

Forces and Weight

• Force: a push or pull that can change the shape or motion of an object. Force is measured in newtons (N).
• Weight: the force of gravity on an object. Weight = mass × gravitational field strength (W = mg, g ≈ 10 N/kg).
• Free fall: motion under gravity alone, with no air resistance. Objects fall with the same acceleration.
• Newton's first law: an object stays at rest or keeps moving at constant velocity unless a resultant force acts on it.
• Newton's second law: resultant force = mass × acceleration (F = ma).
• Friction: a force that opposes motion between surfaces in contact.

Density, Pressure and Moments

• Density: mass per unit volume. Density = mass ÷ volume.
• Pressure: force per unit area. Pressure = force ÷ area, measured in pascals (Pa).
• Atmospheric pressure: the pressure of the air around us, which is about 100 000 Pa at sea level.
• Moment: the turning effect of a force. Moment = force × perpendicular distance from the pivot.
• Centre of mass: the point where an object's weight appears to act. An object is more stable when its centre of mass is low and its base is wide.
• Hooke's law: extension is proportional to the force applied, up to the limit of proportionality.
• Simple machines: tools such as levers, pulleys and inclined planes that make work easier by changing the size or direction of a force.

Common slips

• Mixing up mass (kg) and weight (N).
• Forgetting to convert units, such as cm to m or g to kg, before calculating.
• Thinking a moving object needs a force to keep moving; it does not, unless friction or other forces act.
• Reading a measuring cylinder from the top of the meniscus instead of the bottom.
• Confusing speed (scalar) with velocity (vector).