Kinematics and Dynamics

Table Of Contents

1 Units

Sum or difference is called resultant of vectors.
Tip to Tail method: for A + B join the tip of A to the tail of B
Subtraction is simply flipping the sign of the vector]
Multiplication by a constant: only changes magnitude or can make direction antiparallel

Dot Product used for two vectors multiplying to get a scalar: A ° B = (A)(B)cosθ
Cross Product: for two vectors multiplied to get another vector: AxB = (A)(B)sinθ
- Right Hand Rule can be used to determine the direction

Displacement is a vector that is a straight line from point A to point B. Does not take into account the pathway taken
Velocity is also a vector and is defined as the rate of change of displacement in a given unit of time.
Speed is the rate of actual distance travelled in a given unit of time
Instantaneous speed will always equal to the magnitude of the instantaneous velocity

Force is a vector quantity that is experienced as pushing or pulling on objects.
- Gravity is an attractive force felt by all matter. Do not have much significance on a smaller scale, but are significant on the planetary scale.
  - Fg = (Gm1m2)/r^2
  - G = 6.67×10^-11 (Nm^2)/(kg^2)
- Friction is a force that opposes movement of objects. This always forces an object to slow down
  - Static Friction (f_s): stationary object and surface it rests on
    - 0 ≤ fs ≤ μs
  - Kinetic Friction: sliding object and surface it slides over.
    - fk = μk x N
  - Value of static coefficient is always larger than that of kinetic.
Mass is a measure of a body inertia – the amount of matter in the object (scalar).
Weight is a gravitational force so it is a vector quantity. Fg = mg
- Can be thought of as being applied to a single point (center of gravity)
- xcm = Σ (mixi)/mi
Acceleration is the rate of change of velocity that an object experiences as a result of some applied force.

First law states that a body at rest or in motion with a constant velocity will remain that way unless a force is acted upon it. Net force is equal to zero when acceleration is 0.
Second law states that Fnet = ma
Third Law states that for every action there is an equal and opposite reaction.

A ball falling from the sky can be considered linear motion if air resistance is neglected. Terminal Velocity is not reached and the ball is in free fall. Most common format of linear constant acceleration motion.
If air resistance is not neglected, it will oppose the motion of the object. Resistance increases as velocity increases and the object is subject to higher drag forces. When the drag force is equal to the weight of the object, the object stops accelerating since the net force is zero. This velocity is the terminal velocity.

In uniform circular motion the instantaneous velocity vector is always tangent to the circular path. The inertia of the object wants it to continue going straight, but this is stopped by the centripetal force, which is always pointed radially inwards.
- Can resolve components into radial and tangential components. Tangential force is zero in uniform circular motion.
- Fc = (mv^2)/r is the magnitude of the centripital force

Always draw FBD’s to start a force question
Translation equilibrium is when the force causes an object to move without causing any rotation.
- Only exists when the vector sum of all forces acting on an object are zero (first condition of equilibrium).
Rotational equilibrium occurs when forces are applied against an object so that the object rotates around a pivot point (fulcrum).
- Generates a torque or the moment of force. Lever arm is the distance between the applied force and the fulcrum.
- τ = r x F = rFsinθ

Rotational equilibrium only occurs when the second condition of equilibrium is met. The vector sum of all torques acting on an object must be zero.