When considering equilibrium, just focus on the force applied to the ball. For the law of action and reaction, however, you need to consider both the ball and the hand.

The resultant force is also called the net force.

The first law (law of inertia): A body at rest tends to stay at rest unless acted upon by an outside net force. A body in motion tends to stay in motion at a constant velocity unless acted on by an outside net force.
The second law (law of acceleration): The net force on an object is equal to the mass of the object multiplied by its acceleration.
The third law (law of action and reaction): For every action there is an equal and opposite reaction.

When an object impacts another object, both objects receive a force of the same magnitude but in opposite directions.

Between two objects, there is an attractive force proportional to the product of the objects' masses and inversely proportional to the distance between them, raised to the second power.



When mass is doubled, acceleration is reduced to half.

The sine of the angle is equal to the ratio of the opposite side to the hypotenuse. The cosine is equal to the ratio of the adjacent side to the hypotenuse. The tangent is the ratio of the opposite side to the adjacent side.

When a force is imposed on an object, that object starts moving with a uniform acceleration proportional to the net force applied and inversely proportional to its mass.

Strictly speaking, because the earth is not a perfect sphere, gravitational acceleration close to the earth's surface varies slightly, depending on the location. Even so, you can safely approximate this value as 9.8 m/s^2.



Let's examine it in detail.

The momentum of an object varies as an external force is imposed on it, and a change in momentum is called impulse.

We can easily apply the law of conservation of momentum in two ideal situations - a perfectly elastic collision, or a perfectly inelastic one. The first example here was a perfectly elastic one - two objects that move separately after their collision, losing no energy in the process. Think of an elastic collision as something like two super-balls hitting each other - in the real world, the collision of atoms is said to be elastic. An inelastic collision is one where the colliding objects combine to form a singular object in motion after their collision.

We'll look at this in more detail in the next chapter.



Work is equal to displacement of an object multiplied by the component of force applied in the same direction.

The work to lift a load using a ramp must be equal to the work to lift that load straight upward. Also, please note that our results are the same, regardless of the angle of the ramp.

The change in kinetic energy is equal to the work done on the object.

We can also derive this equation another way.

Why is this so? See expression on page...

Then if you simply multiply both sides by 1/2, you're there!

The braking distance is proportional to the speed raised to the second power. When the initial speed is doubled, the braking distance is quadrupled.

However, in order for this law to hold true, we must consider air resistance and other friction to be negligible.

Air resistance can be thought of as collisions with molecules of air, which gives them kinetic energy. This is a change in energy. In this case, the law of conservation of energy is still working - just at a microscopic level!

The kinetic energy the ball has at its launching point must equal the potential energy it has at its height.

Due to the conservation of energy, we know that the sum of the mechanical energy must stay the same at all intermediate points on this slope.

At the same height, kinetic energy is equivalent even if the orientation of velocity is different.

Of course, it'd be impossible to go beyond that original height of h.

And if you've come to be fond of physics, even if just a little, I'm glad too.

As 1/2 does not affect the units, you can omit it when determining the units.

1J represents energy generated from work that moves an object by 1m and continues to impose a force of 1N on it.

1 joule is equivalent to the energy required to lift a 102g object directly upward 1 meter.

1 calorie (1cal) represents the thermal energy required for increasing the temperature of 1 gram of water by 1C under 1 atmosphere of pressure (1atm). Relative to a joule, this unit is defined as follows: 1cal = 4.2J.

The elasticity of rubber originates in the activity of polymer molecules to recover the initial state with a greater "disorder," where they are very closely curled up, after a state with a lower "disorder," in which molecules are expanded and aligned.

Not all forces can be expressed as having a potential. Forces such as these are said to be nonconservative.

The normal force is simply the force perpendicular to the surface a body travels on.

The coefficient of friction is simply a measure of how "sticky" two surfaces are.

And the equation above isn't true in every case. This is simply the maximum possible force exerted by friction on the object.

And because the 100 yen coin has no initial momentum in the y direction, we know that the momentum of both coins in the y direction must offset each other.

It's not possible to find exact solutions, since we have too many variables to solve for and not enough equations. However, we can explore the relationships between these variables.

Additionally, assign theta=0 for this expression, and you'll find v1=v2. This is relevant to a case where object 1 passes by object 2 without colliding.

Velocity is the first derivative of distance, and acceleration is the second derivative of distance (both with respect to time).