CAIE Physics IGCSE Topic 1: Motion, Forces and Energy Summary Notes

Physical Quantities and Measurement Techniques

• A ruler (rule) is used to measure the length of an object between $1\,mm$ and $1\,m$.

• A micrometer screw gauge is used to measure very small distances that a rule cannot measure.

  • As the screw is turned, the gauge’s jaws move to fit around the object.

  • The integer value in $mm$ is read on the inner cylinder.

  • The decimal value to $0.01\,mm$ is read on the rotating barrel.

• A measuring cylinder is used to measure the volume of a liquid or an object that can sink.

  • Placing an object into a measuring cylinder full of water causes the water level to rise; this rise is equal to the volume of the object.

  • For regular shaped solids, volume can also be found by calculation.

• Clocks and timers (both analogue and digital) are used to measure time intervals.

• Averaging techniques are used to measure short distances or time intervals to reduce percentage uncertainty, which is higher for smaller measurements.

  • This usually requires repeat measurements.

  • For the period of a pendulum, one measurement is taken for several oscillations and then a mean is calculated.

Scalar and Vector Quantities

• A scalar quantity has magnitude only.

• A vector quantity has magnitude and direction and can be represented by arrows.

• Scalar Examples:

  • Distance

  • Speed

  • Time

  • Mass

  • Energy

  • Temperature

• Vector Examples:

  • Displacement

  • Velocity

  • Acceleration

  • Momentum

  • Force

  • Electrical/gravitational field strength

• Combining Vectors at Right Angles:

  • Vectors can be combined into one resultant vector for forces and velocities.

  • Graphically: Vectors are drawn to scale as arrows at right angles (length represents magnitude). A diagonal drawn from their origin gives the resultant.

  • By Calculation: The magnitude of the resultant is found using Pythagoras’ theorem: $a^2 + b^2 = c^2$ . The direction is found using trigonometry.

Motion Definitions and Equations

• Speed is defined as the distance travelled per unit time:

  • $\text{speed} = \frac{\text{distance travelled}}{\text{time}}$

  • Units: $m/s$

• Velocity is the speed in a given direction:

  • $\text{velocity} = \frac{\text{displacement}}{\text{time}}$

  • $v = \frac{s}{t}$

  • Units: $m/s$

• Acceleration is the rate of change of velocity:

  • $\text{acceleration} = \frac{\text{change in velocity}}{\text{change in time}}$

  • $a = \frac{\Delta v}{\Delta t}$

  • Units: $m/s^2$

• Deceleration is a negative acceleration.

• Average Speed is calculated when speed is changing (accelerating or decelerating):

  • $\text{average speed} = \frac{\text{total distance travelled}}{\text{total time}}$

• Unit Consistency: Always double-check and convert units before calculation.

  • Distance/displacement: $mm$, $cm$, $m$, or $km$.

  • Time: $ms$, $s$, minutes, or hours.

  • Standard answers are usually in metres ($m$) and seconds ($s$).

Interpreting Displacement-Time Graphs

• The gradient represents the velocity (or speed on a distance-time graph).

  • $\text{speed or velocity} = \text{gradient} = \frac{\text{change in } Y}{\text{change in } x}$

  • If calculated for a curved section, the answer is the average speed.

• Specific Line Characteristics:

  • Horizontal line: The object is at rest.

  • Straight diagonal line: The object is moving at a constant speed/velocity.

  • Curved line with increasing gradient: The object is accelerating.

  • Curved line with decreasing gradient: The object is decelerating.

  • Negative gradient: The object is returning to the starting point.

Interpreting Velocity-Time Graphs

• The gradient represents acceleration.

  • $\text{acceleration} = \text{gradient} = \frac{\text{change in } y}{\text{change in } x}$

• Specific Line Characteristics:

  • Speed/velocity is zero: The object is at rest.

  • Horizontal line: The object is moving at a constant speed (acceleration is zero).

  • Positive gradient: The object is accelerating.

  • Negative gradient: The object is decelerating.

  • Straight line: The object is moving with constant acceleration.

  • Curved line: The object is moving with changing acceleration.

• The area under the graph gives the distance travelled.

  • To calculate this, split the area into rectangles and triangles.

Free Fall and Terminal Velocity

• Gravitational constant ($g$): Approximately $9.8\,m/s^2$.

• Free fall in a vacuum: Objects falling in a uniform gravitational field in the absence of air/liquid resistance fall with the same constant acceleration of $9.8\,m/s^2$.

• Free fall with resistance: Objects falling in the presence of air or liquid resistance fall with decreasing acceleration.

• Process of reaching Terminal Velocity:

  • 1. Initially, there is no air resistance and the only force is weight ($a = 9.8\,m/s^2$).

  • 2. As the object accelerates, speed increases, which increases air resistance.

  • 3. This increases the upward force, decreasing the downward resultant force; thus, acceleration decreases.

  • 4. Eventually, weight and air resistance become equal and opposite.

  • 5. Resultant force becomes zero, acceleration becomes zero, and terminal velocity is reached.

• Equivalence of $g$: Gravitational field strength ($9.8\,N/kg$) and acceleration of free fall ($9.8\,m/s^2$) are numerically equivalent.

Mass and Weight

• Mass measures how much matter is in an object (when at rest relative to the observer). Units: $kg$.

• Weight is the gravitational force acting on objects with mass. Units: Newtons ($N$).

• Gravitational field strength ($g$) is the amount of gravitational force (weight) acting on an object per unit of its mass.

  • $\text{gravitational field strength} = \frac{\text{weight}}{\text{mass}}$

  • $g = \frac{W}{m}$

• Planetary Differences: The value of $g$ differs from planet to planet, so an object’s weight differs by location, but its mass remains constant.

• Comparison: The weight and mass of two different objects can be compared using a balance because $g$ is constant at any given location on Earth.

Density

• Density is defined as the mass per unit volume of an object:

  • $\text{density} = \frac{\text{mass}}{\text{volume}}$

  • $\rho = \frac{m}{V}$

  • Units: $kg/m^3$ (or $g/cm^3$).

• Finding the density of a liquid:

  • 1. Measure the mass using a balance: $\text{liquid's mass} = \text{mass of cylinder full of water} - \text{mass of empty cylinder}$.

  • 2. Measure the volume by reading the cylinder level.

  • 3. Calculate density using $\rho = \frac{m}{V}$.

• Finding the density of a solid:

  • 1. Measure the mass using a balance.

  • 2. Calculate the volume:

    • Regularly shaped solids: Measure dimensions and use volume equations (e.g., $l \times w \times h$).

    • Irregularly shaped solids (Displacement method): Place the object in a measuring cylinder full of water. $\text{solid's volume} = \text{water's volume with object} - \text{water's volume without object}$.

  • 3. Calculate density using $\rho = \frac{m}{V}$.

• Floating and Sinking:

  • An object floats if it is less dense than the liquid and sinks if it is more dense.

  • The density of water is $1\,g/cm^3$. Objects with density > 1\,g/cm^3 sink; those with density < 1\,g/cm^3 float.

  • For two immiscible liquids, the less dense liquid will float on top of the denser one.

Effects of Forces and Hooke’s Law

• Size and Shape: Forces can change the size and shape of an object. Elastic solids return to their original shape/size when force is removed.

• Hooke’s Law: The spring constant is the force required per unit of extension.

  • $\text{spring constant} = \frac{\text{force applied}}{\text{extension}}$

  • $k = \frac{F}{x}$

  • Units: $N/m$

• Experimental Investigation of Extension:

  • 1. Measure initial length with a ruler.

  • 2. Attach masses incrementally (adding force) and record the new length after each addition.

  • 3. $\text{Extension} = \text{new length} - \text{initial length}$.

  • 4. Repeat 3 times and find average extension for each mass.

  • 5. Calculate force as weight: $\text{Force} = \text{mass} \times 9.8\,N/kg$.

  • 6. Plot force and extension on a load-extension graph.

• Load-Extension Graphs:

  • Should be linear and pass through the origin for elastic objects.

  • The gradient of the linear section is the spring constant ($k$).

  • Limit of Proportionality: The point where the graph stops being linear. Beyond this point, the object stretches irreversibly and $k = \frac{F}{x}$ no longer applies.

Resultant Forces and Newton’s Laws

• Resultant Force: A single force describing the combined action of all forces acting on an object.

  • Linear resultant: $\text{sum of forces in one direction} - \text{sum of forces in opposite direction}$.

• Newton’s First Law: Without a resultant force (forces balance each other out), an object remains at rest or continues in a straight line at a constant velocity.

• Newton’s Second Law: With a resultant force, an object's velocity will change (acceleration). Acceleration is proportional to resultant force and inversely proportional to mass.

  • $\text{force} = \text{mass} \times \text{acceleration}$

  • $F = ma$

• Circular Motion:

  • Moving in a circle involves constant change in direction, requiring a constant change in velocity (acceleration).

  • This requires a resultant force acting perpendicular to the direction of motion (e.g., gravity for orbits).

  • If mass and radius are constant: increasing force increases speed.

  • If mass and speed are constant: increasing force decreases radius.

  • If mass increases: increased force is required to keep speed and radius constant.

• Friction (Drag): A force between two surfaces that impedes motion and results in heating. It applies to objects moving through liquids or gases (air resistance).

Turning Effect of Forces (Moments)

• Pivot Point: The point about which an object can rotate.

• Rotation:

  • Force applied in same line as pivot = No rotation.

  • Force applied in different line to pivot = Rotation in the direction of the force.

• Moment of a force: A measure of the turning effect.

  • $\text{moment of a force} = \text{force} \times \text{perpendicular distance}$

  • $\text{moment} = Fd$

  • Perpendicular Distance: Length of the object if force is perpendicular; otherwise found using trigonometry.

• Equilibrium: When the clockwise moment equals the anticlockwise moment, there is no resultant moment and the object is balanced.

  • Examples: A bike pedal arm turning around its pivot; a balanced see-saw where the weights of two people create equal moments.

• Multiple Forces: If there are multiple forces on either side, compare the sum of anticlockwise moments to the sum of clockwise moments.

• Equilibrium Experiment:

  • 1. Pivot a uniform ruler at its centre.

  • 2. Place different masses at varying distances until it balances.

  • 3. Calculate $\text{force} = \text{mass} \times 9.18\,N/kg$ (Note: page 14 specifically cited $9.18\,N/kg$ for this calculation).

  • 4. Calculate clockwise and anticlockwise moments to show they are equal.