Kinematics and Dynamics Flashcards
Vectors
physical quantitates that have both magnitude and direction. this includes displacement, velocity acceleration, and force, among others.
Scalars
quantities that are without direction. This may be the magnitude of vectors like speed, or may be dimensionless, like coefficients of friction.
How is vector addition accomplished?
Using tip to tail method or by breaking a vector into its components and using the pythagorean theorem.
V = sqr (X^2 +Y^2 )
How is vector subtraction accomplished?
Changing the direction of the subtracted vector and then following the procedure for vector addition.
What happens when you multiply a vector by scalar changes?
the magnitude may change and may reverse the direction.
What is the dot product?
The dot product is the product of the vectors’ magnitudes and the cosine of the angle between them. Multiplying the two vectors using this process results in scalar quantities.
A x B = [A]{B]cos θ
what is cross product?
The product of the vectors’ magnitudes and the sine of the angle between them. The right-hand rule is used to determine the resultant vectors’ direction. This produces a vector quantity.
A x B = [A][B] sin θ
What is displacement?
the vector representation of a change in position. It is path independent and is equivalent to the straight line distance between the start and end locations.
Distance
a scalar quantity that reflects the path traveled.
velocity
vector representation of the change in displacement with respect to time.
Average velocity
the total displacement divided by the total time.
V= Δx/Δt . V has a line above it
average speed
the total distance traveled divided by the total time.
instantaneous velocity
is limit of the change in displacement over time as the change in time approaches zero.
V= limit Δt –>0 Δx/Δt
instantaneous speed
the magnitude of the instantaneous velocity vector
force
any push or pull that has the potential to result in an acceleration
gravity
attractive force between two objects as a result of their masses.
friction
is a force that opposes motion as a function of electrostatic interactions at the surface between two objects
static friction
exists between two objects that are not in motion relative to each other. Can take on many values.
kinetic friction
between two objects that are in motion relative to each other. It is a constant value.
coefficient of friction
depends on the two materials in contact.
Mass
measure of the inertia of an object, the amount of material.
Weight
the force experienced by a given mass due to the gravitational attraction to the earth
acceleration
the vector representation of the change in velocity over tie. Average or instantaneous acceleration may both be considered, similar to velocity.
Newton’s first law, or law of inertia
an object will remain at rest or move with a constant velocity if there is no net force on the object.
Fnet = ma = 0
Newton’s second law
any acceleration is the result of the sum of the forces actin on the object and its mass.
Fnet = ma
Newton’s third law
any two objects interacting with one another experience equal and opposite forces as a result of their interaction
F AB = – F AB .
linear motion
free fall and motion in which the velocity and acceleration vectors are parallel or antiparallel.
projectile motion
contains both and x and y component. assuming negligible air resistance, the only force actin on the object is gravity.
inclined planes
two dimensional movement. It is often the easiest to consider the dimensions as being parallel and perpendicular to the surface of the plane.
circular motion
the best thought of as having radial and tangential dimensions. In uniform circular motion, the only force is the centripetal force, pointing radially inward. Instantaneous velocity vector always points tangentially
free body diagrams
representations of forces acting on an object. they are useful for equilibrium and dynamics problems.
translational equilibrium
occurs int eh absence of any net forces actin on an object. An object in translational equilibrium has a constant velocity, and may or may not also be in rotational equilibrium
Rotational equilibrium
occurs in the absence of any net torques actin on an object. rotational motion may consider any pivot point, but the center of mass is most common. An object in rotational equilibrium has a constant angular velocity; on the MCAT, the angular velocity is usually zero.
component vector equation
X = V cos θ Y= V sin θ
Determination of direction from component vectors?
θ =tan^-1 Y/X
Universal gravitation equation
Fg = Gm1m2/r^2
Static friction
0≤ fs ≤ μsN
Kinetic Friction
fk = μkN
Force of gravity (weight on earth)
Fg = mg
Center of mass
x = m1x1 +m2x2 + m3x3/ m1 + m2 + m3 . same for y or z
average acceleration
a =Δv/Δt
Kinematics, no displacement
V=Vo + at
kinematics (no final velocity)
x = Vot + at^2/2 .
kinematics no time
V^2 = Vo^2 + 2ax
kinematics no acceleration
x = vt . v is average velcoity .
components of gravity
Fpara = mg sin θ
F perp = mg cos θ
Centripetal force
Fc = mv^2/r
torque .
τ = r x F = rF sinθ
