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$KE = \frac{1}{2}mv^2$, where $KE$ is kinetic energy, $m$ is mass, and $v$ is velocity.

A state where the sum of forces and the sum of moments (torques) on a body are zero.

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

$F = -kx$, where $F$ is force, $k$ is the spring constant, and $x$ is the displacement from equilibrium.

$P = \frac{F}{A}$, where $P$ is pressure, $F$ is the normal force, and $A$ is the area over which the force is distributed.

$MA = \frac{F_{out}}{F_{in}}$, where $MA$ is mechanical advantage, $F_{out}$ is the output force, and $F_{in}$ is the input force.

$\sum \tau = 0$, indicating that the sum of all moments (torques) about a pivot point is zero, and the object is in rotational equilibrium.

The rate of change of velocity of an object; measured in meters per second squared ($m/s^2$).

$f_s \leq \mu_s N$, where $f_s$ is the static friction force, $\mu_s$ is the coefficient of static friction, and $N$ is the normal force.

The force transmitted through a string, rope, cable or wire when it is pulled tight by forces acting from opposite ends.

$F_c = \frac{mv^2}{r}$, where $F_c$ is centripetal force, $m$ is mass, $v$ is velocity, and $r$ is the radius of the circular path.

$PE = mgh$, where $PE$ is potential energy, $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height above a reference point.

A vector quantity that tends to accelerate an object; measured in Newtons ($N$).

The resistance to motion of one object moving relative to another.

$P = \frac{W}{t}$, where $P$ is power, $W$ is work done, and $t$ is the time taken.

A simple machine used to change the direction of a force and potentially multiply its magnitude.

$E = \frac{\sigma}{\varepsilon}$, where $E$ is Young's Modulus, $\sigma$ is stress, and $\varepsilon$ is strain.

$\tau = \frac{F}{A}$, where $\tau$ is shear stress, $F$ is the force applied parallel to the surface, and $A$ is the area over which the force is applied.

$W = mg$, where $W$ is weight, $m$ is mass, and $g$ is acceleration due to gravity.

$J = F\Delta t$, where $J$ is impulse, $F$ is the average force applied, and $\Delta t$ is the time interval over which the force is applied.

$p = mv$, where $p$ is momentum, $m$ is mass, and $v$ is velocity.

The moment that induces bending in an object along an axis; occurs due to external forces or moments.

$\rho = \frac{m}{V}$, where $\rho$ is density, $m$ is mass, and $V$ is volume.

$F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration.

The component of contact force perpendicular to the surface; it prevents objects from passing through each other.

$W = Fd\cos(\theta)$, where $W$ is work done, $F$ is force, $d$ is displacement, and $\theta$ is the angle between the force and displacement vectors.

$L = I\omega$, where $L$ is angular momentum, $I$ is moment of inertia, and $\omega$ is angular velocity.

A scalar quantity representing the amount of matter in an object; measured in kilograms ($kg$).

The twisting of an object due to an applied torque that tends to produce rotational deformation.

For every action, there is an equal and opposite reaction.

$\tau = rF\sin(\theta)$, where $\tau$ is the torque, $r$ is the position vector (distance from the pivot), $F$ is the force, and $\theta$ is the angle between $r$ and $F$.

$f_k = \mu_k N$, where $f_k$ is the kinetic friction force, $\mu_k$ is the coefficient of kinetic friction, and $N$ is the normal force.

$a_c = \frac{v^2}{r}$, where $a_c$ is centripetal acceleration, $v$ is velocity, and $r$ is the radius of the circular path.

A scalar measure of an object's resistance to rotational acceleration, dependent on the mass distribution with respect to the axis of rotation.

$\sum \vec{F} = 0$, indicating that the sum of all forces on a body is zero, hence the body is at rest or moving with constant velocity.

$\varepsilon = \frac{\Delta L}{L_0}$, where $\varepsilon$ is strain, $\Delta L$ is the change in length, and $L_0$ is the original length.

The change in length, area, or volume of a material due to change in temperature.

$\sigma = \frac{F}{A}$, where $\sigma$ is stress, $F$ is the force acting on an area, and $A$ is the area.

The upward force exerted by a fluid that opposes the weight of an immersed object.