Kinematics and Dynamics
Velocity
Uniform Velocity
Motion with a constant speed and constant direction
Constant velocity means a net force of zero, according to Newton's first law of motion
Vector Quantity
The total displacement travelled over a period of time
Represented in meters per second with direction, m/s [direction]
Vav= Δd/Δt= d2-d1/Δt
Velocity= displacement/time
Position-Time Graph
Slope of a position-time graph will give you the velocity
When the data is not linear, draw a tangent line at a given time
Slope of the tangent line will give you the instantaneous velocity at the specific time
Acceleration-Time Graph
The area under the line or curve in an acceleration-time graph will give you the velocity
Acceleration
Vector quantity
The rate of change of velocity with respect to time
Represented in meters per second squared, m/s^2 [direction]
a=∆v/∆t= final velocity - initial velocity/∆t
Acceleration= velocity/time
Velocity-Time Graph
Slope of a velocity-time graph will give you the acceleration
Acceleration due to gravity
Any object falling freely near Earth will accelerate at 9.80m/s^2 [down]
Also part of Newton's second law, where it is directly proportional with the net force
Inversely proportional to mass according to Newton's second law
Kinematic Equations
Five different equation consisting of different variables, where you are able to isolate and find an unknown variable
v2=v1+a∆t
∆d=1/2(v1+v2 )∆t
∆d=v1∆t+1/2a∆t^2
v2^2= v1^2+2a∆d
∆d=v2∆t-1/2a∆t^2
Variables include initial and final velocity, displacement/distance, time, and acceleration
Can be used to solve the acceleration for Newton's second law
Motion in 2D
Diagram
Objects can move in two dimensions, such as in horizontal plane and a vertical plane
The compass rose can be used to express directions in a horizontal plane, such as [N 40° W]
To determine total displacement in two dimensions, displacement vectors can be added together using a scale diagram. To add two or more vectors together, join them tip to tail and draw the resultant vector from the tail of the first vector to the tip of the last vector
Algebraic
Sketch the vector diagram and label it
Break all vectors into x and y components
Add all x components, then add all y components
Find the resultant using the Pythagorean theorem
Find the angle using tan
Projectiles
Projectile motion consists of independent horizontal and vertical motions
The horizontal and vertical motions of a projectile take the same amount of time
Projectiles move horizontally at a constant velocity
Projectiles undergo uniform acceleration in the vertical direction, due to gravity
Objects can be projected horizontally or at an angle to the horizontal.
Projectile motion can begin and end at the same or at different heights
The five kinematic equations of motion can be used to solve projectile motion problems
Newton's Laws
Newton's First Law
All objects will remain in a state of rest or continue to move with a constant velocity unless acted upon by an unbalanced force
Net Force= 0
Velocity would be linear on a velocity-time graph, indicating it is constant
Newton's Second Law
An object will accelerate in the direction of the net force
The magnitude of the acceleration is directly proportional to the net force acting on it and inversely proportional to its mass
Fnet= ma
Acceleration can also be found using the kinematic equations, when given other variables
Newton's Third Law
For every action force there is a simultaneous reaction force that is equal in magnitude and opposite in direction
Basic kinematic problems are approached using Newton's laws of motion
Displacement
Displacement is a vector quantity- has both magnitude and direction
Direction is represented in terms of direction in square brackets, [N], [S], [W], [E].
Represented in meters along with direction, m [direction]
Refers to the change in an object's position
∆d=Final displacement-intial displacement
Velocity- time graph
Displacement can be found by calculating the area under the curve or line of the velocity-time graph
Distance
Scalar quantity- quantity with only magnitude
The total length of the path travelled by an object in motion
Represented in meters, m
"d"= distance
Speed
Scalar Quantity
Only has magnitude
The total distance travelled over a period of time
Represented in meters per second, m/s
Vav=Δd/Δt
Speed= distance/time
Forces
Applied Force
A force that results when one object makes contact with another and pushed or pulls it
Any contact force not already described
Force of Gravity
The force of attraction between any two objects due to their mass.
Fg= mg
g= 9.80 m/s^2
Acceleration due to gravity (kinematics)
Normal Force
A pushing force exerted by a surface on an object
Always acts away from and perpendicular to the surface
Tension
The force exerted by materials that can be stretched.
Ex: ropes, strings, cables, etc
Friction
A force of resistance
Always acts opposite to the motion or attempted motion of an object
Free Body Diagram
A simple drawing representing the object and all forces acting on it
Net Force
The sum of all forces acting on an object
Must add the x and y forces seperately
Gravitational Force
Exists between any two masses
Electromagnetic Force
Caused by electric charge
Strong Nuclear Force
Keeps protons and neutrons together
Weak Nuclear Force
Involves nuclear decay transmutation
Friction
Static Friction
Force that acts against attempted motion to prevent the sliding of one surface relative to another
Kinetic Friction
Force that acts against the motion of an object
Depends on the mass of the object, type of surface, and type of material
Coefficient of friction
Ff= uFn
Us= Fs/Fn
Uk= Fk/Fn
Free Fall
The motion of a falling object where only the force of gravity is acting on it
Terminal Speed
The maximum constant speed of a falling object
Uniform velocity as it has constant speed and will be falling in the same direction; downwards
Air Resistance
Type of friction
Increases as cross-sectional area increases
Increases when speed increases
Gravitational Field Strength
Force field
A region of space around an object that exerts a force on the other object within that region
The force per unit mass acting on an object when placed in a gravitational field
9.80 N/kg [down]
Mass
The amount of matter in an object (kg)
Weight
Measure of the force of gravity on the object (N)
Weightlessness
Force of gravity is still acting but both the object and frame of reference are in free fall