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

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

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

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

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.
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 ($$\vecphy{J}$$ 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, $$\text{kg m/s}$$.