# Credit

This unit is worth 90 UMS, which equates to 15% of the A2 credit.

# Assessment

It is examined by a single 60-mark 1h15m written exam in either January or May/June.

# Content

## Module 1 : Newton’s laws and momentum

*The ideas developed by Newton underpin work in a number of the units and modules at A2. The second law in particular has impact on several topics including the behaviour of gases in the module on thermal physics. This module provides the opportunity to discuss the use of models to explain the elaborate physical world around us. It is also important to remember that a fundamental law such as Newton’s second law is valid as long as a single experiment does not contradict it. For objects travelling at relatively slow speeds, its success is truly phenomenal, but strange things start to happen when objects travel at speeds close to the speed of light. There are many opportunities for students to carry out experimental work and analyse data using ICT or data-logging techniques.*

**Newton’s laws of motion**

*Candidates should be able to:*

- state and use each of Newton's three laws of motion;
- define linear momentum as the product of mass and velocity and appreciate the vector nature of momentum;
- define net force on a body as equal to rate of change of its momentum;
- select and apply the equation F = Δp / Δt to solve problems;
- explain that F = ma is a special case of Newton’s second law when mass m remains constant;
- define impulse of a force;
- recall that the area under a force against time graph is equal to impulse;
- recall and use the equation impulse = change in momentum.

**Collisions**

*Candidates should be able to:*

- state the principle of conservation of momentum;
- apply the principle of conservation of momentum to solve problems when bodies interact in one dimension;
- define a perfectly elastic collision and an inelastic collision;
- explain that whilst the momentum of a system is always conserved in the interaction between bodies, some change in kinetic energy usually occurs.

## Module 2 : Circular motion and oscillations

*There are many examples of objects travelling at constant speed in circles, eg planets, artificial satellites, charged particles in a magnetic field, etc. The physics in all these cases can be described using the ideas developed by Newton. We can use the models created by Newton to understand and predict the motion of artificial satellites around the Earth and the planets in our own solar system. The atoms in a solid and the piston of a car both show oscillatory motion. In this module, we develop the physics behind oscillatory motion and illustrate its beneficial and detrimental effects. This module provides ample opportunities to show how theories are developed. Newton’s thought experiment on the cannon ball fired at right angles to the Earth’s gravitational field can be used to show how scientific ideas and models can be developed to describe the motion of satellites in geostationary orbits.*

**Circular motion**

*Candidates should be able to:*

- define the radian;
- convert angles from degrees into radians and vice versa;
- explain that a force perpendicular to the velocity of an object will make the object describe a circular path;
- explain what is meant by centripetal acceleration and centripetal force;
- select and apply the equations for speed v = 2$\pi$r / T and centripetal acceleration a = v
^{2}/ r; - select and apply the equation for centripetal force F = ma = mv
^{2}/ r.

**Gravitational Fields**

*Candidates should be able to:*

- describe how a mass creates a gravitational field in the space around it;
- define gravitational field strength as force per unit mass;
- use gravitational field lines to represent a gravitational field;
- state Newton’s law of gravitation;
- select and use the equation F = - GMm / r
^{2}for the force between two point or spherical objects; - select and apply the equation g = - GM / r
^{2}for the gravitational field strength of a point mass; - select and use the equation g = - GM / r
^{2}to determine the mass of the Earth or another similar object; - explain that close to the Earth’s surface the gravitational field strength is uniform and approximately equal to the acceleration of free fall;
- analyse circular orbits in an inverse square law field by relating the gravitational force to the centripetal acceleration it causes;
- define and use the period of an object describing a circle;
- derive the equation $T^{2}=\left ( \frac{4\pi ^{2}}{GM} \right )r^{3}$ from first principles;
- select and apply the equation $T^{2}=\left ( \frac{4\pi ^{2}}{GM} \right )r^{3}$ for planets and satellites (natural and artificial);
- select and apply Kepler’s third law T
^{2}∝ r^{3}to solve problems; - define geostationary orbit of a satellite and state the uses of such satellites.

**Simple harmonic oscillations**

*Candidates should be able to:*

- describe simple examples of free oscillations;
- define and use the terms displacement, amplitude, period, frequency, angular frequency and phase difference;
- select and use the equation period = 1/frequency;
- define simple harmonic motion;
- select and apply the equation a = – (2$\pi$f)x as the defining equation of simple harmonic motion;
- select and use x = Acos(2$\pi$ft) or x = Asin(2$\pi$ft) as solutions to the equation a = – (2$\pi$f)x;
- select and apply the equation v
_{max}= (2$\pi$f)A for the maximum speed of a simple harmonic oscillator; - explain that the period of an object with simple harmonic motion is independent of its amplitude;
- describe, with graphical illustrations, the changes in displacement, velocity and acceleration during simple harmonic motion;
- describe and explain the interchange between kinetic and potential energy during simple harmonic motion;
- describe the effects of damping on an oscillatory system;
- describe practical examples of forced oscillations and resonance;
- describe graphically how the amplitude of a forced oscillation changes with frequency near to the natural frequency of the system;
- describe examples where resonance is useful and other examples where resonance should be avoided.

## Module 3 : Thermal Physics

*In physics, the terms ‘internal energy’ and ‘temperature’ have very precise meanings. The amount of internal energy within an object is the total random kinetic and potential energy of all the atoms within the object whereas temperature is used to determine in which direction energy will flow when two objects are close to one another. The flow of energy from one object at a higher temperature to another object at a lower temperature is called heating. This module uses the ideas of Newtonian mechanics to explain how gas atoms exert pressure on container walls. It provides an opportunity to discuss how scientific models in the form of Newtonian mechanics can be developed to explain the behaviour of gases.*

**Solid, liquid and gas**

*Candidates should be able to:*

- describe solids, liquids and gases in terms of the spacing, ordering and motion of atoms or molecules;
- describe a simple kinetic model for solids, liquids and gases;
- describe an experiment that demonstrates Brownian motion and discuss the evidence for the movement of molecules provided by such an experiment;
- define the term pressure and use the kinetic model to explain the pressure exerted by gases;
- define internal energy as the sum of the random distribution of kinetic and potential energies associated with the molecules of a system;
- explain that the rise in temperature of a body leads to an increase in its internal energy;
- explain that a change of state for a substance leads to changes in its internal energy but not its temperature;
- describe using a simple kinetic model for matter the terms melting, boiling and evaporation.

**Temperature**

*Candidates should be able to:*

- explain that thermal energy is transferred from a region of higher temperature to a region of lower temperature;
- explain that regions of equal temperature are in thermal equilibrium;
- describe how there is an absolute scale of temperature that does not depend on the property of any particular substance (ie the thermodynamic scale and the concept of absolute zero);
- convert temperatures measured in kelvin to degrees Celsius (or vice versa) : T (K)= θ (°C) + 273.15;
- state that absolute zero is the temperature at which a substance has minimum internal energy.

**Thermal properties of materials**

*Candidates should be able to:*

- capacity;
- select and apply the equation E = mcΔθ;
- describe an electrical experiment to determine the specific heat capacity of a solid or a liquid;
- describe what is meant by the terms latent heat of fusion and latent heat of vaporisation.

**Ideal gases**

*Candidates should be able to:*

- state Boyle’s law;
- select and apply pV / T = constant;
- state the basic assumptions of the kinetic theory of gases;
- state that one mole of any substance contains 6.02 × 10
^{23}particles and that 6.02 × 10^{23}mol^{-1}is the Avogadro constant N_{A}; - select and solve problems using the ideal gas equation expressed as pV = NkT and pV = nRT, where N is the number of atoms and n is the number of moles;
- explain that the mean translational kinetic energy of an atom of an ideal gas is directly proportional to the temperature of the gas in kelvin;
- select and apply the equation E = (3/2) kT for the mean translational kinetic energy of atoms.

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