1: Units and Kinematics Flashcards
The SI system is also called
The MKS System
SI unit for length
Meter (m)
SI unit for mass
kilogram (kg)
SI unit for force
Newton (N)
SI unit for time
second (s)
SI unit for Work and Energy
Joule (J)
SI unit for power
Watt (W)
giga-
10^9
mega-
10^6
kilo-
10^3
centi-
10^-2
milli-
10^-3
micro-
10^-6
nano-
10^-9
pico-
10^-12
Convention for expressing numbers that simplifies calculations and standardizes results
Scientific Notation
- Makes math without a calculator more doable
- Multiplying: multiply coefficients and add exponents
- Dividing: Divide coefficients and subtract second exponent from first exponent
- Square: Square the coefficient and and multiply the exponent by 2
If your answer choices are all different by a power of 10 or more,
Make your work easier by rounding, without worrying about getting too close to another answer choice
Sin of 0
0
Sin of 30
1/2
Sin of 45
(sq. rt. of 2) / 2
Sin of 60
(sq. rt. of 3) / 2
Sin of 90
1
Sin of 180
0
Cos of 0
1
Cos of 30
(sq. rt. 3) / 2
Cos of 45
(sq. rt. 2) / 2
Cos of 60
1/2
Cos of 90
0
Cos of 180
-1
Sin
Opposite over hypotenuse
Cos
Adjacent over hypontenuse
Tan
Opposite over adjacent
Logarithm
The power to which that bar must be raised to equal that number.
A base raised by some power will equal a number, and that power is the logarithm of that number to that particular base.
e
2.71828
Common log
Use the base 10 log
Natural log (ln)
use the value of e (2.71828)
Purpose of log and ln
Allowing for the expression of vast range of values along a condensed and manageable scale
log (mn)=
log m + log n
log (m/n)=
log m - log n
log (m^n)=
(n) log m
Vectors
Numbers that have magnitude and direction
-Displacement, velocity, acceleration, force
Scalars
Numbers that have only magnitude
- distance, speed, energy, pressure, mass
End up back at starting point
Displacement = 0
Resultant
Sum or difference of two or more vectors
- When adding vectors, add tip to tail
Anything that can exist without a direction is
Scalar
-If it does’t matter which direction you approached from or which direction you are going
Most common Pythagorean triples
3: 4:5
5: 12:13
If we know X and Y, we can find V by using
the Pythagorean theorem
When you subtract vectors
You are simply flipping the direction of the vector being subtracted and then following the same rule of adding tip to tail
Vectors can be multiplied by a scalar (n) to change
length, direction, or both
- If (n) is positive, B and A are in the same direction
- If (n) is negative, B and A are in opposite directions
Displacement
A change in an object’s position in space
- Object must be in motion
- This is a vector quantity
Displacement does not account for
the pathway
Velocity
Its magnitude is measured as the rate of change of displacement in a given unit of time
- Vector
- Direction is the same as the direction of the displacement
- SI units are meters/second
Speed
The rate of actual distance traveled in a given time
- Scalar
Instantaneous speed
Is always equal to the magnitude of the objects instantaneous velocity, which is a measure of the average velocity as the change in time approached 0
- Scalar
Average velocity
The ratio of the displacement vector over the change in time
-Vector
Average speed
The ratio of the total distance traveled over the change in time
- Accounts for actual distance traveled
Acceleration
The rate of change of velocity over time
- Vector
- Results from application of force(s)
Average acceleration, a (with a line over the a)
The change in instantaneous velocity over the change in time
Instantaneous acceleration, a
The average acceleration as delta t approaches 0
If slope is positive (velocity vs. time)
Acceleration is positive and in the direction of velocity
If slope is negative (velocity vs. time)
Deceleration and in the opposite direction of velocity
If you see force on the MCAT
think acceleration (and vice versus) F=ma
Falling objects exhibit
Linear motion with constant acceleration
- One-dimensional
Free fall
When an object falls with a constant acceleration (the acceleration due to gravity (g), 9.8 m.s^2) and does not reach terminal velocity
Terminal velocity is due to
The upward force of air resistance equaling the downward force of gravity. As the net force on the object at this point becomes zero, the acceleration is also zero. The object remains at a constant velocity until it is acted upon by another force.
Alway make “up”
Positive and “down” negative
Projectile motion
Motion that follows a path along two dimensions
Objects in projectile motion on earth experience
The force and acceleration of gravity only in the vertical direction
- So Vy will change at the rate of g, but Vx will not
- On the MCAT you will be able to assume that horizontal velocity (Vx) will be constant, because we assumed that air resistance is negligible
Whenever an object reaches its maximum height
Its vertical velocity will be zero for the brief instant that it stops going up and starts falling down. As soon as an object is “in flight” the only force acting on it will be gravity; thus an objects acceleration will be -9.8 m/s^2 the entire time it is in flight.
The amount of time that it takes an object to get to its maximum height is
The same time it takes for the object to fall back down.
- So solve for max height by setting your final velocity to 0 and multiply your answer by two to get the total time in flight
- By multiplying the time by the x-velocity, you can find the horizontal distance traveled
