What kinematics says about an object
-position
- velocity
-acceleration
Linear motion
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Only describe position after a frame of reference is determined
Linear motion choose a single axis x for horizontal and y for either vertical or tilted
2-D motion ( projectile motion ) either in a xy-coordinate system
Important to note where the origin is hence direction
Position equals displacement
Delta x equals x final minus initial
Could be positive or negative
How does the velocity change
Motion diagrams
Three positions with three different velocities with different lengths shows three different
velocities
The way in which the velocity gets bigger the greater the velocity
Accelerate means velocity is changing
Therefore could be speeding up slowing down or simply changing direction
Average over interval of time
Change in displacement over a time interval
Acceleration is a change of velocity over a time interval
How to find the instantaneous velocities ---- use the kinematics equations
First equation is the instantaneous velocity
Second is position at a moment of time
The equations can only be used when the acceleration is constant
Can be used if the equation is zero or no change in velocity however all result in one equation
of x=vt
What do the graphs represent
Position time graph - average velocity (slope) area
Velocity time graph slope- acceleration area displacement ---- if
The top is not half way in the second half of the time you can only travel
2-d motion problem
Relate the velocity of the higher object to the lower object from the height
X direction has constant velocity and y direction has constant acceleration
Area of acceleration time graph is the change in velocity
Key points
Always sketch a motion diagram
Sketch a graph velocity time graph position and acceleration
Determine if a constant velocity means accel equal 0
Can’t say the motion is constant can only use kinematics if accel is constant
Dynamics
Why objects accelerate or don’t ?
Forces push or pull on an object
Forces in physics :
Gravity
Friction
Normal
Tension
Spring
Force of gravity – field force therefore no physical contact fg = mg
9.8 an place near earths surface
Normal force perpendicular to the surface as long as there is contact there is normal force
Could be in any direction
Friction force acts parallel sometimes friction is ignored
Sliding kinetic friction
Not moving / not sliding = static friction
Mu times fn ( kinetic friction)
Mu times fn is greater than or equal to than mu time normal force ( static friction)
Kinetic friction –
Opposite to relative motion of the object
Tension = force that string can put on an object
Spring depends how much it is compressed or stretched
Direction of the force is always opposite the direction in which the length of the spring has
changed
Fs = kx
Free body diagrams a representation of all forces even I f a pushing force draw it as if it’s a
pulling force
There may be forces at angles
Newtons first and second law –
Key question – is the object at rest or moving at a constant velocity
Forces mut be balanced for net force to be zero
Acceleration therefore forces are unbalanced
Direction of net force is direction of acceleration
F=ma
Newtons third law equal and opposite forces --- an interaction between two objects
The interatiactions make up the action reaction pair
Equal and opposite
When you draw a free body diagram an action reaction pair is not drawn
Circular motion and gravitation unit three
Circular motion
What does acceleration measure
How fast an objects velocity changes
Acceleration rate at which velocity changes
Velocity
Speeds up
Slows down
Or changes direction
Circular motion deals with the change of direction of an object’s velocity
If speed doesn’t change it is called uniform circular motion
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Velocity is always tangent to the path
Acceleration is perpendicular to acceleration so that speed doesn’t change?
Acceleration is always centripetal (pointing to the center)
Centripetal acceleration is proportional to the square of the speed of the object and
inversely proportional to the radius of the circular path
Net force is reffered to as centripetal force
Tension when the yoyo is at the top of the path
Freebody diagram both tension and gravity pointing down
F net = ma
To maintain circular motion the tension. On the string at the tip of the path must be at least
zero
Solving for velocity when tension is zero yields the minimum speed for the yoyo to stay at a
circular path at the top
V = square root of rg
At the bottom of the path
Direction of the net force is different
Tension is greater at the bottom of the circle than it is up top
Uniform circular motion
Period – time for one revolution
Frequency – number of revolutions per seconds
Speed the magnitude of velocity = v= distance / time
2pi R / T or 2pi R f
Gravitation –
Any two forces have a force of gravity towards each other
Directly related to the masses they
Inversely related to the square of the center-to-center distance between the objects THE
INVERSE SQUARE RULE
G is the force of gravity divided by the mass
Gravitational field of any object is equal to g times the mass of that object divided by the radius
squared
When really close to the planet the center-to-center distance is usually the radius of the planet
Inverse square relationship the distance increases by 2 squared or by 4
X component is ft sin of the angle and y component if ft cosine of the angle
Ft cos theta = mg
Normal force is equal to the component of the weight
Fg parallel = Mg sin theta
Perpendicular = mg cos theta
Work and energy
Forces cause change in velocity
Change in the momentum of an object system
Change in energy of an object or system
Energy the ability to cause change and can be stored different ways
Force and position graph
Force divided by x equals k(spring constant ) --- slope
Area – work
Spring potential – upward parabola because of x squared
Mechanical energy constant if no external forces - ( nice straight horizontal line)
Kinetic energy opposite of the spring potential energy - opposite of spring potential
Forces simply interaction between two objects
System external changes change the total amount of energy
Work is parallel force to displacement fd times the angle ( cosine theta)
Momentum and impulse –
Impulse must act on a an object in order to act on an object
Impulse is related to the force and the duration od the time a force acts on ana object
Total momentum of a closed system is a conserved quantity
Measures mass in motion
In order to change the velocity a net force must act on the object
Momentum is related to newtons second law
Mv is the change in the momentum of an object
F times the change in time is the impulse that acts on an object and has the same direction as
the net force
Change in momentum of an object equals the impulse acting upon it
Can also be viewed as an action reaction pair ---- newtons third law
Conservation of momentum
In a closed system the momentum of the system will remain constant
Momentum
Collisions / explosions
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If a 2d collision the momentum needs to be applied in both the x direction and the y
direction separately
Area of force time graph equals impulse
Long force over short time
Small force over long time
Simple harmonic motion
Amplitude and period are dependent on each other
Equilibrium is where there is no net force
If you displace the object from equilibrium a restoring force will accelerate the object towards
the equilibrium position
Maximum displacement from equilibrium is called the amplitude
Mg sin theta is the restoring force
Restoring force is hookes law
Restoring force graph – hookes law points towards ( equilibrium)
f/d gives is the spring constant
energy in simple harmonic motion
kinetic energy moving with the greatest speed --- therefore in the middle
what affects the period Is a pendulum – ( period the time it takes to complete one oscillation)
the length the pendulum
gravitational field
spring is impacted by k constant and mass the greater the mass the greater the period
both multiplied by 2 pi