A-Level Mechanics Formula Sheet Annotated Cheat Sheet

Key Facts

• For constant acceleration, the SUVAT equations are $v = u + at$, $s = ut + \frac{1}{2}at^2$, $v^2 = u^2 + 2as$, and $s = \frac{(u+v)t}{2}$.
• Newton’s second law states that resultant force is $F_{\text{net}} = ma$, where $F_{\text{net}}$ is in newtons, $m$ is in kilograms, and $a$ is in $\text{m s}^{-2}$.
• Weight is the gravitational force on a mass and is given by $W = mg$, where $g \approx 9.81\,\text{m s}^{-2}$ near Earth’s surface.
• Momentum is $p = mv$, and conservation of momentum means $\sum p_{\text{before}} = \sum p_{\text{after}}$ when no external resultant force acts.
• Impulse equals change in momentum, so $J = F\Delta t = \Delta p = m(v-u)$ for a constant force.
• Work done by a constant force is $W = Fs\cos\theta$, and kinetic energy is $E_k = \frac{1}{2}mv^2$.
• For circular motion at constant speed, centripetal acceleration is $a = \frac{v^2}{r} = \omega^2 r$ and centripetal force is $F = \frac{mv^2}{r}$.
• The moment of a force about a pivot is $M = Fd$, where $d$ is the perpendicular distance from the pivot to the line of action of the force.

Vocabulary

Displacement

Displacement is the vector distance from an object’s starting position to its final position.

Acceleration

Acceleration is the rate of change of velocity, given by $a = \frac{\Delta v}{\Delta t}$.

Resultant Force

Resultant force is the single overall force that has the same effect as all forces acting together.

Momentum

Momentum is the product of mass and velocity, given by $p = mv$.

Impulse

Impulse is the product of force and time and equals the change in momentum, $J = F\Delta t = \Delta p$.

Moment

A moment is the turning effect of a force about a pivot, calculated using $M = Fd$.