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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.

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

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

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

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

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

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

$\tau = rF\sin(\theta)$, 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 $F$.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$J = F\Delta t$, 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.

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

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

$\tau = \frac{F}{A}$, 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.

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

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

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

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

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

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

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

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.

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