# SPH4U Grade 12 Physics Kinematics, Dynamics, & Circular Motion Test

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/s2

• 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

Fd=CdPAV2

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

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: VAX = VAY + VYX
• Where Y is common in both Vectors
• Y is eliminated and leaves for AX, the final answer
• Subtracting Vectors, Example: VAX = VAY – VXY
• Add the subtracted vector by reversing the subscripts
• VAX = VAY + VYX
• Lastly, use Vector component or Cosine Law to add the vectors (magnitude and direction)

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

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

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: this thing that makes stuff stay at constant speed, is a fundamental property of matter
• 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: net is zero but it’s at constant speed
• Third Law: for every action, there is a reaction, equal in magnitude but opposite in direction.

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

ac=v2/r

• r = radius
• v = speed of object

ac = v2/r = 4(pi)2r/T2 = 4(pi)2rf2

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

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.

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.