#### Forces and Moments

**FORCES**

- Forces are measured in Newtons;
*Force*=*Mass*×*Acceleration* - 1 Newton is the amount of force needed to give 1 kg an acceleration of 1 m/s
^{2}

**Effects of Forces**

- A force may produce a change in size and shape of a body; give acceleration or deceleration or a change in direction depending on the direction of the force.
- If there is no resultant force acting on a body, it either remains at rest or continues at constant speeds in a straight line.

**Friction**

- Friction is the force between two surfaces which impedes motion and results in heating.
- Air resistance is a form of friction.

**Hooke’s Law **

Stress-Strain Curve* (Photo Credit: *Quora.com)

- Springs extend in proportion to load, as long as they are under their proportional limit.
- Limit of Proportionality: is the point at which the load and extension are no longer proportional.
- Elastic Limit: is the point at which the spring will not return to its original shape after being stretched.
*Load (N)*=*Spring Constant*×*Extension**F*=*ke*

**Circular Motion**

- An object at a steady speed in a circular orbit is always accelerating as its direction changes, but it gets no closer to the center.
*Centripetal force*is the force acting towards the center of a circle. It is a force that is needed for circular motion, not caused by circular motion.- For example, when you swing a ball on a string in a circle, the tension of the string is the centripetal force. If the string is cut, then the ball will travel in a straight line at a tangent to the circle at the point where the string was cut.
*Centrifugal Force*is the force acting away from the center of a circle. This is what make a slingshot go outwards as you spin it.- The centrifugal force is the reaction to the centripetal force. It has the same magnitude but is opposite in direction to the centripetal force.
*F*=^{mv2}/_{r}

**Newton’s Law**

*First Law of Motion*: If no external force is acting on an object, the object will, if stationary, remain stationary, and if in motion, will remain in motion.*Second Law of Motion*: F = ma*Third Law of Motion*: If an object A exerts a force on an object B, then the object B will exert an equal but opposite force on object A.

**MOMENT**

*Moment (Nm)*=*Force (N)*×*Distance from Pivot (m)*- In equilibrium, clockwise moment = anticlockwise moment.
- Increasing the force or distance from the pivot would increase the moment of a force.
- Levers are force multipliers:
- Turning a bolt is far easier with a wrench because the distance from the pivot is massively increased, and so is the turning effect.

**Center of Mass**

- Center of mass is an imaginary point in a body where the total mass of the body seems to be acting.
- How to work out the center of mass of a card:
- Mark three points on the edge of the card
- Make a hole using a pin on each point
- Hang it on a cork board and make a line when it is stable
- Do this for all three points
- Where all three lines intersect is the center of mass.

**Stability**

- An object will be in stable equilibrium when it returns to its original position after given a small displacement.
- For an object to start rotating, it needs to have an unbalanced moment acting on it.

**Scalars and Vectors**

- A scalar is a quantity that only has a magnitude (so it can only be positive); e.g. speed.
- A vector quantity has a direction as well as a magnitude; e.g. velocity, which can be negative.