Kinematics and Dynamics Flashcards
British/Imperial System (FPS)
Foot, Pound, Second
rarely used by MCAT
Metric Systm (MKS)
Length -> Meter Mass -> Kilogram Time -> Second Current -> Ampere Mole -> Mol Temperature -> Kelvin Luminous Intensity -> Candela
Base vs Derived Units
B: standard units a system is designed around (seconds, kgs)
D: base units associated together (newton, joule, watt) for force, energy and power)
Angstroms
1 A = 10^-10 m
Electron volt
energy gained by an electron accelerating through a 1 V potential difference
1eV = 1.6*10^-19
Vectors (Bold)
numbers with magnitude and direction (displacement, velocity, acceleration, force)
Scalars (italic)
numbers only with magnitude
distance, speed, energy, mass, pressure
Resultant
sum or difference of two or more vectors
sum of A and B is to place tail of B at tip of A, the sum will be tail of A to the tip of B
Right Traingle for Vectors
V = Hyp
X and Y
X = Vcos theta Y = V sin theta
V = X^2 + Y^2
Angle of Resultant Vector
theta = tan^-1 (Y/X)
Steps to Finding Results via Components
1) Resolve vectors into X and Y components
2) add all x components for Rx ; add all y components for Ry
3) Magnitude of resultant is sqrt(Rx^2 + Ry^2)
4) Direction is theta= tan-1 (Ry/Rx)
Vector Subtraction
like addition but subtract all x components from each toher and all y components from each other
A - B = A + (-B)
Multiplying Vectors by scalars
R = (n) A where n = scalar
magnitude is A* abs(n)
direction depends on sign where negative n is opposite directions and positive n is same direction
If vector A is multiplied by scalar -3, then new Vector B is…
three times as long as A and in opposite directions
Multiplying 2 Vectors: Dot Product
develops scalar quantity like work (F * D)
A * B = (A)(B) cos (theta)
where ( ) is the resultant value of the vectors ex: sqrt (Ax^2 + Ay^2)
Multiplying 2 Vectors: Cross Product
when generating a third vector and needing its magnitude and direction like torque
A x B = (A) (B) sin (theta)
where ( ) is the resultant value of the vectors ex: sqrt (Ax^2 + Ay^2)
**use right hand rule to determine the direction!
The resultant of a cross product will always be ____ to the plane created by the two vectors
perpendicular
Displacement (x)
an object in motion may experience a change in its position in space.
Vector quantity, ONLY NET CHANGE DOESNT CONSIDER PATH
Distance (d)
considers path taken and is a scalar quantity compared to displacement
Velocity (v)
vector and is the rate of change of displacement in given time
(m/s)
Speed
distance traveled in a given time
Instantaneous Speed vs Instantaneous Velocity
IS is equal to the magnitude of IV
Instantaneous Velocity
V = lim as t -> 0 of dx/dt
Average Velocity
V = delta x / delta t
where delta x is change in position
Average Speed
v = d/t
Force
vector quantity causing a pushing or pulling between two objects that are not necessarily touching
Newtons
Gravity
attractive force felt by all forms of matter
all objects exert a gravitational force on each other
Magnitude of Gravitational Force
F = ( Gm1m2 )/ (r^2)
r is distance between the two center of massses
Friction
force that opposes the movement of objects
two types: statc and kinetic
Static Friction (fs)
between a stationary object and surface
0 < fs < usN
ranges between 0 and the max force generated from static friction coefficient and normal force
Coefficient of Static Friction
unitless quantity dependant on the two materials in contact
Kinetic Friction (fk)
SLIDING object and material it slides over
fk = ukN
always constant value! smaller than us
Difference between us and uk
uK is always smaller than uS and is constant
Mass (m)
amount of matter in the object, body’s inertia
scalar and independent of gravity
Weight (Fg)
measure of gravitational force on a objects mass
Newtons
Fg = m*g
Only for a ____ body with ___ shape and uniform density can the center of gravity be located in the _____
homegenous symetrical, center
Acceleration (a)
rate of change of velocity an object experiences as a result of some applied force
vector quantty
a = dV/dt
Instantaneous Acceleration
a = lim as t -> 0 of dV/dT
Tangent line of V vs T graph is….is positiv slope…if negative slope….
acceleration
aceeleration is positive and in direction of velocity
acceleration is negative and against velocity
Newtons First Law
F = ma = 0
Law of Inertia
body either at rest or in motion with constant velocity will remain as such unless a net force acts on it.
Newtons Second Law
F=ma
An object of mass m will accelerate when vector sum of the forces results in some nonzero resultant force vector
Newtons Third Law
Fab == - Fab
To every action there is an opposed but equal reaction
no physical contact is necessary
Linear Motion
objects velocity and acceleration are along the line of motion so object continues in a straight line
not just vertical or horizontal
One Dimensional Equations
v = vo + at
x =Vot + (at^2)/2
V^2 = vo^2 + 2ax
x = Vt
z = displacement V = average velocity
During free fall problems, the velocity when ball is at its maximum height is ___
0!
Air resistance increases as the speed of an object _____ , the object ten experiences _______ as the magnitude of velocity increases. Eventually, this will be equal in magnitude to the weight of the object and object will fall with constant velocity according to newtons 1st law known as _______
increases, drag force, terminal velocity
Projectile Motion
follows a path along 2 dimensions with velocities and accelerations in two directions that are independent of one another
vy changes at rate gravity but vx will remain constant!!
Inclined Planes
motion in two directions
Fgx = mgsin(theta)
Fgy = mgcos(theta)
Circular Motion
force causes object to move in circular pathway, displacement in one loop is 0
Uniform Circular Motion
instantaneous velocity vector is tangent to circular path, meaning inertia makes it want to escape in a tangent path
Centripetal Force
force radially inward which prevents object from escaping uniform circular motion
Fc =( mv^2 )/ r
In uniform circular motion, the tangential force is _____ because there is no change in the ___ of the object
0 , speed
Centripetal acceleration
generated by the centripetal force
Translational Motion
force causes an object to move without any rotation, usually linear
Translational Equilibirum
vector sum of all the forces acting on an object is equal to zero, similar to Newtons first law
object will have constant velocity: a constant speed (0 or non zero value) and a constant direction
Rotational Motion
when forces applied against an object cause object to rotate around a pivot point known as fulcrium
Torque
moment of force
r x F = rF sin (theta)
r = length of lever arm
Rotational Equilibrium
vector sum of all torques is equal to 0
clockwise = negative
counterclockwise = positive
