How forces affect motion

Force

A push or pull on an object that can alter its state of rest, motion, direction, or shape; modeled by $F = ma$ and measured in newtons ($\text{N}$).

Balanced forces

Forces acting on an object that are equal in magnitude and opposite in direction, producing zero acceleration and maintaining constant velocity. F=0

Unbalanced forces

Forces whose vector sum does not equal zero, causing an object to accelerate by speeding up, slowing down, or changing direction. F≠0

Weight

The gravitational force exerted on an object by Earth (or another body), calculated as $W = mg$ and directed vertically downward toward Earth's center.

Normal force

The contact support force exerted by a surface perpendicular to an object resting on it; equal to $N = mg$ on a flat horizontal plane without additional vertical forces.

Friction

The contact force opposing relative motion or impending motion between two touching surfaces, calculated as $f = \mu N$.

Newton's first law of motion

The object at rest remains at rest and an object in motion continuous to move with constant velocity and less and at force acts upon the object the force acting on an object is zero the acceleration cannot begin to move or change it velocity in such case its acceleration is zero.

Inertia

The inherent tendency of an object to resist changes to its state of rest or uniform motion, directly measured by mass ($\text{kg}$).

Newton's second law of motion

When a net force acts on an object the object accelerates in the direction of the net force the magnitude of the acceleration is proportional to the magnitude of the net force and his inversely proportional to the mass of the object. ($F = ma$)

One newton ($1\,\text{N}$)

The amount of net force required to impart an acceleration of $1\,\text{m/s}^2$ to a mass of $1\,\text{kg}$ ($1\,\text{N} = 1\,\text{kg} \times 1\,\text{m/s}^2$).

Linear momentum

The product of an object's mass and its velocity ($p = mv$), possessing vector direction identical to the velocity vector and measured in $\text{kg}\cdot\text{m/s}$.

Impulse

The product of average applied force and time interval ($F \times t$), which equals the overall change in momentum ($mv - mu$) and carries the unit $\text{N}\cdot\text{s}$.

Kinematic reason a fielder pulls hands back when catching a ball

Extending the stopping time ($t$) decreases the rate of change of momentum, significantly reducing the impact force ($F = \frac{mv - mu}{t}$) on the hands.

Newton's third law of motion

Whenever one object is exerting a force on a second object the second object is silent initially exciting and equal and opposite force on the first object.

Gun recoil velocity formula

$v_g = -\frac{m_b v_b}{m_g}$, derived from the principle of conservation of momentum where total initial momentum of the system is zero.

Thrust in rocket propulsion

The forward reaction force produced by ejecting mass backward at high speed, calculated as $F = \left(\frac{\Delta m}{\Delta t}\right) \times v$.

Acceleration of a multi-body connected system

$a = \frac{F_{\text{net}}}{m_1 + m_2 + \dots}$, determined solely by external forces because internal action-reaction tension pairs cancel out.