# Main concepts in dynamics

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 $$\text{kg m/s}.$$

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 $$1\text{ N}=1\text{ kg}\times\text{ m/s}^2$$.

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

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.

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.

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, $$\text{kg m/s}$$.