**Grade 12 Physics – Kinematics and Dynamics Notes**

**Displacement:** a vector form of a distance

**Velocity:** a change in displacement over time

- Slope of secant from a displacement – time graph

**Instantaneous Velocity:** exact speed at that point in time

- Tangent curve of a velocity – time graph

**Calculating Vectors**

**Vectors:** a unit with magnitude and direction

- They are resultant to vertical and horizontal movements
- Calculated through trigonometry:
- Head to Tail: when one vector connects to another
- Head to Head: when vectors start at the same point
- Vector Components
- Break vectors into their X Y components.
- Add individual X Y components, then find resultant

**Acceleration**

**Earth: **accelerates object towards center at 9.8 m/s^{2}

- Slight differences due to shape of the earth, but atmosphere has no impact

**Drag: **falling objects encounter some amount of air friction

- Density of air will be factor

F_{d}=C_{d}PAV^{2}

- Cd: co-efficient of drag
- P: density of air
- A: surface area of object
- V: speed of subject

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**Terminal Speed:** when Fg = Fd, a = 0, Fnet = 0, so it will be at constant speed.

**Field of Reference**

- The speed an object is moving at is dictated in relation from where you’re viewing it.
- Example: A boat may be travelling 30m/s relative to the water, but only 20m/s relative to the ground because it’s influenced by the water’s 10m/s current.
- Viewed from ground is different from viewing it from the water.

**Calculating with field of Reference**

- General Formula: V
_{AX }= V_{AY}+ V_{YX}- Where Y is common in both Vectors
- Y is eliminated and leaves for AX, the final answer
- Subtracting Vectors, Example: V
_{AX }= V_{AY}– V_{XY}- Add the subtracted vector by reversing the subscripts
- V
_{AX }= V_{AY}+ V_{YX} - Lastly, use Vector component or Cosine Law to add the vectors (magnitude and direction)

- V

- Add the subtracted vector by reversing the subscripts

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**Forces**

- A net force causes objects to accelerate/decelerate
- When forces act in opposite directions, they add to zero
- Eg. Normal force counteract a surface, preventing items from falling through it.
**Free body diagrams:**shows all forces acting on an object- Useful when solving forces problems, should be drawn at all times

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**Inclined Planes**

- When blocks are placed on a plane, consider the surface parallel to the plane x.
- And consider the plane perpendicular to the plane to by y.
- Use vector components to break gravity and solve problem

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**Newton’s Laws and Pulley Problems**

**First Law:**an object in motion stays in motion unless there is a force that slows it down**Inertia:****Second Law:**states that force can be affected by mass and acceleration**Force = Mass * Acceleration****Static Equilibrium:**net force is zero and it doesn’t move**Dynamic Equilibrium:****Third Law:**for every action, there is a reaction, equal in magnitude but opposite in direction.

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**Circular Motion**

**Circular Motion:**occurs when an object is travelling in a circular path with a fixed radius and speed.- Since direction is changing every moment in a circle, velocity changes, so the object will accelerate towards the center

a_{c}=v^{2}/r

- r = radius
- v = speed of object

a_{c }= v^{2}/r = 4(pi)^{2}r/T^{2} = 4(pi)^{2}rf^{2}

- f = frequency
- T = period
**Centripetal force:**the force created by circular motion towards the center.- Centripetal force = mass * centripetal acceleration

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**Non-Inertial/Inertial frames of reference**

**Inertial**: when the frame of reference is moving at constant speed and is not accelerating. Newton’s laws are obeyed.**Non-Inertial:**when the frame of reference is under-going acceleration. Newton’s laws aren’t obeyed in this case.- When the frame of reference accelerates forward, net force is moved backwards because we say a
**fictitious force**lifts it**.**

- When the frame of reference accelerates forward, net force is moved backwards because we say a

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**Centrifugal force**

**Centrifugal Force:**another form of fictitious force which is created due to the existence of some other force- If centripetal force accelerates towards the center in circular motion, the centrifugal force will act against the object and whatever inside.