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Further Mechanics 2 formulae

The 18 results the Further Mechanics 2 notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 18, the formulae booklet prints 8, 8 are yours to memorise and 2 are working lines the notes derive in front of you.

Further Maths · 9 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

9 lessons

Angular speed and horizontal circular motion

a = rω^{2} = \frac{v^{2}}{r}

IN THE FORMULAE BOOKLETConditionsCircular motion of radius r. This is the component towards the centre; if the speed varies there is a tangential component as well.

\tan θ = \frac{v^{2}}{rg}

NOT IN THE BOOKLET: LEARN ITConditionsA particle on a smooth banked track, or a conical pendulum, moving in a horizontal circle at constant speed v. Once friction acts, this design speed no longer applies.

Motion in a vertical circle

T - mg\cos θ = \frac{mv^{2}}{r}

NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsResolving towards the centre for a particle on a light inextensible string of length r, θ measured from the lowest point, and valid only while the string stays taut.

Centre of mass of a discrete distribution

\text{mean x} = \frac{Σ m_{i}x_{i}}{Σ m_{i}}, \qquad \text{mean y} = \frac{Σ m_{i}y_{i}}{Σ m_{i}}

NOT IN THE BOOKLET: LEARN ITConditionsA non-zero total mass, with the particles coplanar and all coordinates measured from one origin.

Centres of mass of plane figures and frameworks

\text{Triangular lamina: } \tfrac{2}{3} \text{ along the median from the vertex}

IN THE FORMULAE BOOKLETConditionsA uniform triangular lamina.

\text{Circular arc, radius } r, \text{ angle at centre } 2α: \frac{r \sin α}{α} \text{ from the centre}

IN THE FORMULAE BOOKLETConditionsA uniform circular arc, with α in radians.

\text{Sector of a circle, radius } r, \text{ angle at centre } 2α: \frac{2r \sin α}{3α} \text{ from the centre}

IN THE FORMULAE BOOKLETConditionsA uniform sector of a circle, with α in radians.

\text{Solid hemisphere, radius } r: \tfrac{3}{8}r \text{ from the centre}

IN THE FORMULAE BOOKLETConditionsA uniform solid hemisphere.

\text{Hemispherical shell, radius } r: \tfrac{1}{2}r \text{ from the centre}

IN THE FORMULAE BOOKLETConditionsA uniform hemispherical shell.

\text{Solid cone or pyramid, height } h: \tfrac{1}{4}h \text{ above the base, on the line from the centre of the base to the vertex}

IN THE FORMULAE BOOKLETConditionsA uniform solid cone or pyramid.

\text{Conical shell, height } h: \tfrac{1}{3}h \text{ above the base, on the same line}

IN THE FORMULAE BOOKLETConditionsA uniform conical shell.

Centres of mass by integration

\text{mean x} = \frac{\text{∫} xy \, dx}{\text{∫} y \, dx}, \qquad \text{mean y} = \frac{\text{∫} \frac{1}{2}y^{2} \, dx}{\text{∫} y \, dx}

NOT IN THE BOOKLET: LEARN ITConditionsA uniform lamina bounded by y = f(x), the x-axis and the limits, with y ≥ 0 across the interval.

\text{mean x} = \frac{\text{∫} x y^{2} \, dx}{\text{∫} y^{2} \, dx}

NOT IN THE BOOKLET: LEARN ITConditionsA uniform solid of revolution, formed by rotating y = f(x) through a full turn about the x-axis.

Newton's laws with a variable force

F(x) = mv\frac{dv}{dx}, \qquad F(t) = m\frac{dv}{dt}

NOT IN THE BOOKLET: LEARN ITConditionsMotion in a straight line. Use the dv/dx form when the force is given in terms of x or v, and the dv/dt form when it is given in terms of t or v.

Simple harmonic motion

\frac{d^{2}x}{dt^{2}} = -ω^{2}x

NOT IN THE BOOKLET: LEARN ITConditionsSimple harmonic motion: the acceleration must be proportional to the displacement from a fixed point and directed towards it, with ω > 0.

v^{2} = ω^{2}(a^{2} - x^{2})

NOT IN THE BOOKLET: LEARN ITConditionsThe same simple harmonic motion, a the amplitude and x measured from the centre of the oscillation, so |x| ≤ a.

Oscillations on strings and springs

m\frac{d^{2}x}{dt^{2}} = -\frac{λ x}{l}, \qquad ω^{2} = \frac{λ}{ml}

NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsx measured from the equilibrium position rather than the natural length, and the string must stay taut throughout; a spring may be compressed, a string may not.

Further kinematics: acceleration as a function of x, t or v

\frac{dv}{dt} = \text{f}(t) \text{ or f}(v), \qquad v\frac{dv}{dx} = \text{f}(v) \text{ or f}(x)

NOT IN THE BOOKLET: LEARN ITConditionsMotion in a straight line, choosing whichever form matches the variable the acceleration is given in.

Every formula in the library is indexed by unit on the equation index, and the Further Mechanics 2 notes are where these results are derived and used. The 8 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Further Mechanics 1 formulae · Decision Mathematics 1 formulae