• Mechanics: the study of motion of objects (including force and energy)

  • Kinematics: how objects move

  • Dynamics: forces, why objects move then way they do

• Motion without rotation is defined as 1D Translational Motion

Systems:

• System: the objects being observed and analyzed

• Anything outside the system is external.

• Anything inside the system is internal.

• If we observe a basketball and a hand, the basketball and hand are the system. The floor it bounces off of is external. The bouncing is internal.

Frames of Reference:

• Frame of reference: a reference point where you compare the system/object to

• To determine position, you need a frame of reference, distance from the frame, and (sometimes) the direction from the frame

Vectors vs Scalars

• Scalars: measurements with a magnitude/numberical value.

• Examples of scalars: mass, time, speed, cost, energy

• Vectors: measurements with a magnitude and a direction

• Examples of vectors: position, displacement, velocity, acceleration

Position

• Position: where an object is located with respect to some reference frame or some point of origin (it’s a vector)

Motion

• Motion is relative to the reference frame.

• You step on a skateboard and hold the basketball at the same position and then skate. Behind you is a stationary telephone. Relative to the telephone, the basketball moves. But since the basketball is the same distance and direction away compared to you, it is not in motion relative to you.

• Distance: the length of the path traveled (scalar)

• Displacement: the change in position (vector) or the distance from the starting point to the ending point

• X (final) - X (initial) = ΔX

• If you travel a maze, the distance you’ve traveled (including dead ends, wrong paths, etc) is the distance. Displacement is how far the ending point is from the starting point.

Center of mass

• Center of mass: specific point where the mass behaves as if it were concentrated

Speed vs Velocity

• Speed: how fast you are moving (scalar)

• Velocity: how fast you move in a particular direction (vector)

Velocity

• Velocity: rate of change of position

• Velocity with a direction is a vector

Average speed

• average speed = distance (m) / time (sec)

Average velocity

• average velocity = change in position / change in time = displacement / time interval

Forces

• Forces: an interaction between two objects/systems (internal and external)

• Causes changes in velocity / motion. Forces don’t have to change motion or velocity, they can be cancelled by other forces

• Left and right forces cancel out. Up and down forces cancel out

• Force is a vector. Measured in Newtons ( 1 N = 1 kg* m/s^2)

Free Body Diagrams

• Free body diagrams: shows all the forces acting on a system. Depicts the center of mass as a dot and draws all external forces starting on the dot

• Motion maps: draws a line with an X for the origin or reference point, and the axis representing the positive direction. Dots are drawn to indicate the object’s position at equal time intervals. Arrows are drawn from the dots to indicate direction/rate of motion. Larger arrows indicate a higher rate of motion

  • An object has a constant velocity / rate if the displacement between the points are constant, and the arrows indicating the velocity is the same length.

  • An object is stationary when the rate/velocity is zero and there is no arrow on the diagram. Instead, there are points underneath each other.

  • If an object begins at some positive position in front of the referent point and moves towards said point, the velocity is negative and the arrows will point left, not right

Acceleration is a vector

• Acceleration: the rate of change in velocity, or how fast velocity is changed and in what direction. Unit is meters per seconds squared

• Average velocity = change in velocity / time required

State of motion

• Constant state of motion refers to an object at rest or an object at constant velocity

• Acceleration means there is a change in motion

• 3 states of motion

  • at rest

  • moving at a constant velocity

  • accelerated motion

Position vs Time

• x = mt + x(0), where x(0) is initial position, v = velocity, and t = time

Average velocity w / uniform acceleration

• v(a) = (v + v(0) / 2) where v(a) = average velocity, v = final velocity, and v(0) = initial velocity

Instantaneous acceleration

• The slope of the velocity graph at a particular time