Newton's laws

In a nutshell

Newton's laws of motion are three very important laws that describe how objects move. They relate the forces that act on an object to the resultant motion of the object. 

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Equations

You need to know the following equation. 

​$$force = mass \times acceleration\\ \ \\F=m\times a$$​​

Variable definitions

Newton's first law

The first law of motion states that there needs to be a resultant force acting on an object in order for it to change its motion. 

A change in its motion could be the object speeding up or slowing down, it could also be the object starting to move from rest. 

If the resultant force on an object is zero, then it will remain in its current state of motion. If it was stationary, then it will remain stationary after the resultant force is applied.  If it was moving, then it will continue to move at the same velocity after the resultant force is applied. 

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Newton's second law

The acceleration that an object experiences is proportional to the resultant force acting on it. It requires more force to accelerate a heavier object, so the acceleration is inversely proportional to the mass of the object. 

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Newton's second law states that:

​$$force = mass \times acceleration$$

​$$f = m \times a$$

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Example

A ball has a mass of $$400 \space grams$$​. If the ball experiences a resultant force of $$10 \space N$$​, what is the acceleration it will experience? 

Write out the quantities you have been given and make sure they are in the correct form: 

​$$m = 400 \space g = 0.4 \space kg$$

$$f = 10 \space N$$

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Then write down the equation you need to use: 

​$$f = m \times a$$

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Rearrange the equation to solve for acceleration instead: 

​$$a = \frac{f}{m}$$​​

Finally, substitute the values into the equation: 

​$$a = \frac{10}{0.4}$$​​

Therefore, the acceleration of the ball is $$\underline{25 m/s\ ^2}$$​.

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Newton's third law

The third law says that when two objects interact with one another, the forces that they exert on each other are equal and opposite. Another way to think about this law is that, for every action, there is an equal and opposite reaction.

Newton's third law must be the same type of force acting on two different objects. 

Example

If a person pushes against a wall, they exert a force onto the wall. As a result, they will experience a reaction force from the wall. This reaction force will push against their hands. It will be a reaction force of the same magnitude as the action, but in the opposite direction.

1. Action 2. Reaction

The forces are the same type but acting on different objects. One is the force of the person on the wall and the other is the wall on the person. This is also an example of Newton's first law as the forces are balanced, which means the person is stationary as they weren't moving beforehand.