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# Main concepts in dynamics

## Momentum

Linear momentum (or simply: momentum, $\vecphy{p}$) is the total quantity of motion of an object and involves both its mass and its velocity. It is a vector quantity.

A long cargo train experiences a greater "quantity of motion" (i.e. momentum) than a small passenger car moving at the same velocity.

Momentum is conserved. In other words, the total momentum of a group of objects before a collision (or some other interaction) is equal to the total momentum after a collision.

The momentum $\vecphy{p}$ of an object is given by the product of its mass $m$ and its velocity $\vecphy{v}$: $$\vecphy{p}=m\vecphy{v}$$

The unit of momentum is $\text{kg m/s}.$

Momentum is transferred when billiard balls strike each other. However, the total momentum is conserved.

## Definition of a force

A force is defined as something that causes acceleration.

Hitting a tennis ball causes the tennis ball to accelerate. The racquet exerts a force on the ball.

Whenever an object accelerates (changes the speed or direction of its movement), a force must be acting on it.

Nails placed near a magnet accelerate towards the magnet. The magnet exerts a force on the nails.

The unit of force is the newton $\text{(N)}$. The newton is defined in SI base units as $1\text{ N}=1\text{ kg}\times\text{ m/s}^2$.

An aircraft needs a force to accelerate on the runway. The force comes from the jet engines.

## Force and acceleration

The force $(F)$ that acts on an object is equal to the product of its mass $\Tblue{(m)}$ and its acceleration $\Tred{(a)}$:

\begin{align*} \text{Force}&= \Tblue{\text{Mass}} \times \Tred{\text{Acceleration}}\\ F&= \Tblue{m} \times \Tred{a} \end{align*}

The object accelerates in the direction of the force applied on it.

Pushing a trolley in the forward direction causes the trolley to accelerate in the forward direction.

A larger force is required to accelerate a larger mass by the same amount. Similarly, a larger force is required to accelerate the same mass by a larger amount.

The force required to roll a boulder is larger than the force needed to roll a beach ball.

A ball dropped from a cliff would take longer to hit the bottom than the same ball thrown downwards.

The force on this object and its acceleration point in the same direction

## Mass resists forces (inertia)

An object's mass describes its tendency to resist changes to its motion or state of rest. This tendency is called inertia.

This means that a force must be applied to change the motion of an object.

A spaceship travelling through space will not slow down unless it experiences a force.

Similarly, a force must be applied to get a stationary object moving.

A stationary ball remains at rest on the ground until it is kicked.

An object with a larger mass requires a larger force to change its motion.

A larger force is required to lift a bowling ball than a ping pong ball. The bowling ball has more mass than a ping pong ball.

Inertia itself is not a force.

Because of its huge mass, an oil tanker strongly resists changes to its velocity. If fully loaded and travelling at maximum speed, it requires over $3 \ukm$ to come to a stop.

## Impulse

Impulse ($\vecphy{J}$ or $\vecphy{I}$) is a quantity measuring the change in momentum. It is a vector quantity.

When you throw a ball, you exert a force on the ball for a short time before letting it go. The total change in momentum during this brief period is the impulse on the ball.

The equation for impulse is: $$\vecphy{J}=\Delta\vecphy{p}=\vecphy{p}_1-\vecphy{p}_0$$

The unit of impulse is the same as the unit of momentum, $\text{kg m/s}$.