Kinematics And Dynamics Flashcards
Units of the British Imperial System
Foot, pounds and second
Metric system units
Meters, kilograms, seconds -> centimetres, grams, seconds
Base units?
Standard units of a measurement system
Derived units?
Fusing or associating base units with each other
Ex: Newton - kg m / s^2
Vectors?
Values that have both magnitude and direction
Scalar?
Value only has magnitude and no direction.
Resultant?
Sum of vectors.
Tip to tail method?
Method of vector addition:
Tail of B to tip of A -> line obtained is the magnitude of A + B
Breaking components?
Method of vector addition:
Vectors broken into horizontal and vertical ie. X and Y / perpendicular and parallel components.
How to find components of vector?
X and Y components can be found from V by drawing right triangle using V as hypotenuse. X is adjacent and Y is opposite.
As cos O = adj by hyp and sin O = opp by hyp ->
X = V cos O and Y = V sin O
Cos O?
Adjacent by hypotenuse
Sin O?
Opposite by hypotenuse
How to obtain vector from components?
Tip to tail method -> use Pythagorean theorem to obtain hypotenuse value.
V^2 = X^2 + Y^2
How to subtract vectors?
Add vector of equal magnitude but opposite direction/sign to first vector.
A - B = A + (-B)
How to multiply vectors and scalars?
- Magnitude will change.
- Value may be anti-parallel (scalar n is -ve) or parallel (n is +ve)
- A*n = B
How to multiply two vectors to obtain a scalar value?
Dot product method
A . B = A x B cos 0
How to multiply two vectors to obtain a vector?
Cross-product method:
A x B = A x B sin 0
How to determine direction of cross product?
C = A x B
Right hand rule - thumb = A, index = B, palm = C
What is displacement?
Object in motion experiencing change in position - ie. Displacement (x or d).
Vector quantity, magnitude and direction.
Linearly connects initial and final position - not actual pathway, net change in position.
Distance?
Change in position in space.
Scalar, magnitude only.
Considers pathway taken.
Velocity?
Vector, magnitude and direction.
Rate of change of displacement in a given unit of time.
SI unit is m/s.
Vector direction same direction displacement.
^X / ^T = V
Speed?
Rate of change of distance in a given unit of time.
Scalar quantity.
^D / ^T = V
Instantaneous velocity and instantaneous speed?
I speed = I velocity magnitude. I speed is scalar.
I velocity is the average velocity as the change in time approaches zero.
Vi = ^X / ^T
[lim ^T -> 0]
Average speed and average velocity?
A speed not always equal to A velocity.
A velocity ratio of X over ^T.
A speed ratio of D over ^T.
Force?
Vector quantity.
Experienced as pushing or pulling.
Exists between objects with a distance in between them.
SI unit is Newton ie. kg m / s^2
Gravity?
Attractive force felt by all of matter.
Fg = Gm1m2 / r^2
G (gravitational constant) = 6.67 x 10 ^-11 Nm^2 / Kg ^2
G inversely proportional r^2.
G proportional m1, m2.
Friction?
Force opposing movement of object - slowing it down to stationary state.
Type: Static friction and kinetic friction.
Static friction?
Experienced between stationary object and surface it rests on.
(Min) 0 <= fs <= Ms N (Max)
Ms = Static friction coefficient
N = Normal force
Applied force less than threshold will not move object.
Kinetic friction?
Force between sliding object and surface it is on.
Fk = Mk N
Fk is constant.
Ms > Mk
Mass?
Amount of matter in an object - independent of gravity.
Scalar quantity.
SI unit is Kg.
Weight?
Measure of gravitational force on mass.
Vector quantity.
SI unit is Newton ie Kg m / s^2
Fg = m g
Fg = weight
g = 9.8 m/s
Centre of mass?
Defined relative to an object or system of objects.
Average position of all the parts of the system, weighted according to their masses.
X = m1x1 + m2x2 / m1 + m2
Acceleration?
Rate of change of velocity of an object due to applied force.
Vector quantity.
SI unit is m/s^2.
If it opposes initial velocity then it causes deceleration.
Avg a = ^V / ^T
Instantaneous acceleration?
Average acceleration as ^T approaches 0.
a = ^V / ^T [lim ^T -> 0]
Velocity vs time?
If slope is downwards ie. -ve, a is -ve.
If slope is upwards ie. +ve, a is +ve.
Newtons 1st law?
A body will remain in rest or constant motion unless a force acts on it.
F net = m a = 0
Newtons 2nd law?
Object of mass m, will accelerate when vector sum is not equal to 0.
F net = m a
F and a are in the same direction.
Newtons 3rd law?
Every force has an equal and opposite reaction.
Fab = -Fba
Types of motion?
Constant (no acceleration) or changing (with acceleration).
Linear motion?
Velocity and acceleration are in the same line of motion, continuing along same line as object.
Linear motion with constant acceleration.
Velocity of object in constant motion?
Vf = vi + at
What is free fall?
Object falling with constant acceleration due to gravity (g = 9.8m/s^2) and would not reach terminal velocity.
What is terminal velocity?
Air resistance opposes object motion, proportionally to object speed - increase in drag force with increase in velocity.
When DF = weight of obj, object falls with constant + terminal velocity.
Projectile motion?
Motion path of object is 2 dimensional. Velocity and acceleration move independent of each other.
Inclined planes?
Motion path of object is 2 dimensional. Force vectors have parallel and perpendicular components (with respect to the plane)
Parallel force vector of inclined plane?
Fg = mgsin0
Perpendicular force vector of inclined plane?
Fg = mgcos0
Circular motion?
Force causes object to move in circular pathway. Hence, displacement of object is 0.
Uniform circular motion?
Vinst is tangential to circular path and is kept in path by inward facing centripetal force.
Centripetal force?
Has a radial and tangential force (0, no change in speed) components. Generates constant acceleration.
Magnitude of centripetal force?
Fc = mv^2/r
Translational equilibrium?
Occurs when forces cause object to move with out rotation. They may be linear, parabolic or inclined.
Translational equilibrium condition?
Vector sum of forces on an object are zero, ie. 1st condition of equilibrium.
Constant velocity, speed and direction.
Rotational equilibrium condition?
Forces applied causing object to move around fixed pivot fulcrum at some distance to generate torque which generates rotational motion.
Torque?
T = r * F = rFsin0
