G484: The Newtonian World

Mr Cowen’s definitive definitions for Newtonian World

Mr Godfrey’s June 2011 Newtonian World walkthrough

Revision videos

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Module 1: Newton’s laws and momentum

4.1.1 Newton’s laws of motion

(a) state and use each of Newton’s three laws of motion;

(b) define linear momentum as the product of mass and velocity and appreciate the vector nature of momentum;

(d) select and apply the equation $F = \frac{\Delta p}{\Delta t}$ to solve problems;

(e) explain that $F = ma$ is a special case of Newton’s second law when mass m remains constant;

(f) define impulse of a force;

(g) recall that the area under a force against time graph is equal to impulse;

(h) recall and use the equation $\mbox{impulse} = \mbox{change in momentum}$ .

4.1.2 Collisions

(a) state the principle of conservation of momentum;

(b) apply the principle of conservation of momentum to solve problems when bodies interact in one dimension;

(d) 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

4.2.1 Circular motion

(a) define the radian;

(b) convert angles from degrees into radians and vice versa;

(d) explain what is meant by centripetal acceleration and centripetal force;

(e) select and apply the equations for speed

$v = \frac{2 \pi r}{T}$

and centripetal acceleration

$a = \frac{v^2}{r}$

(f) select and apply the equation for centripetal force

$F=ma=\frac{mv^2}{r}$

4.2.2 Gravitational fields

(a) describe how a mass creates a gravitational field in the space around it;

(b) define gravitational field strength as force per unit mass;

(d) state Newton’s law of gravitation;

(e) select and use the equation $F = - \frac{GMm}{r^2}$ for the force between two point or spherical objects;

(f) select and apply the equation $g= - \frac{GM}{r^2}$ for the gravitational field strength of a point mass;

(g) select and use the equation $g= - \frac{GM}{r^2}$ to determine the mass of the Earth or another similar object;

(h) explain that close to the Earth’s surface the gravitational field strength is uniform and approximately equal to the acceleration of free fall;

(i) analyse circular orbits in an inverse square law field by relating the gravitational force to the centripetal acceleration it causes;

(j) define and use the period of an object describing a circle;

(k) derive the equation $T^2 = (\frac{4 \pi ^2}{GM})r^3$ from first principles;

(l) select and apply the equation $T^2 = (\frac{4 \pi ^2}{GM})r^3$ for planets and satellites (natural and artificial);

(m) select and apply Kepler’s third law $T^2 \propto r^3$ to solve problems;

(n) define geostationary orbit of a satellite and state the uses of such satellites.

4.2.3 Simple harmonic oscillations

(a) describe simple examples of free oscillations;

(b) define and use the terms displacement, amplitude, period, frequency, angular frequency and phase difference;

$\mbox{period} = \frac{1}{\mbox{frequency}}$

(d) define simple harmonic motion;

(e) select and apply the equation $a = -(2 \pi f)^2 x$ as the defining equation of simple harmonic motion;

(f) select and use $x= A \cos(2 \pi ft)$ or $x= A \sin(2 \pi ft)$ as solutions to the equation $a = -(2 \pi f)^2 x$ ;

(g) select and apply the equation $v_{max} = (2 \pi f)A$ for the maximum speed of a simple harmonic oscillator;

(h) explain that the period of an object with simple harmonic motion is independent of its amplitude;

(i) describe, with graphical illustrations, the changes in displacement, velocity and acceleration during simple harmonic motion;

(j) describe and explain the interchange between kinetic and potential energy during simple harmonic motion;

(k) describe the effects of damping on an oscillatory system;

(l) describe practical examples of forced oscillations and resonance;

(m) describe graphically how the amplitude of a forced oscillation changes with frequency near to the natural frequency of the system;

(n) describe examples where resonance is useful and other examples where resonance should be avoided.

Module 3: Thermal physics

4.3.1 Solid, liquid or gas

(a) describe solids, liquids and gases in terms of the spacing, ordering and motion of atoms or molecules;

(b) describe a simple kinetic model for solids, liquids and gases;

(c) describe an experiment that demonstrates Brownian motion and discuss the evidence for the movement of molecules provided by such an experiment;

(d) define the term pressure and use the kinetic model to explain the pressure exerted by gases;

(e) define internal energy as the sum of the random distribution of kinetic and potential energies associated with the molecules of a system;

(f) explain that the rise in temperature of a body leads to an increase in its internal energy;

(g) explain that a change of state for a substance leads to changes in its internal energy but not its temperature;

(h) describe using a simple kinetic model for matter the terms melting, boiling and evaporation.

4.3.2 Temperature

(a) explain that thermal energy is transferred from a region of higher temperature to a region of lower temperature;

(b) explain that regions of equal temperature are in thermal equilibrium;

(c) 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);

(d) convert temperatures measured in kelvin to degrees Celsius (or vice versa):

$T (K)= \theta (°C) + 273.15$ ;

(e) state that absolute zero is the temperature at which a substance has minimum internal energy.

4.3.4 Ideal gases

(a) state Boyle’s law;

(b) select and apply $p \frac{V}{T} = \mbox{constant}$ ;

(d) state that one mole of any substance contains $6.02 \times 10^{23}$ particles and that $6.02 \times 10^{23} mol^{-1}$ is the Avogadro constant $N_A$ ;