PHYSICS I: VECTORS (CH)
What is the derived SI unit for Force?
Newtons (N) Newtons is a derived unit made from base units. 1 N = (kg*m)/s^2
What is the SI unit for current?
ampere (coulomb/second) (A or amp)
What is the SI unit for luminous intensity?
candela (cd)
What is the SI unit for mass (NOT WEIGHT)?
kilogram (kg)
What is the SI unit for length?
meter (m)
What does the MKS unit system stand for?
meter, kilogram, second
What is the SI unit for amount of substance?
mole (mol)
Velocity
the speed and direction of a moving object. It magnitude is measured as the RATE of CHANGE of DISPLACEMENT in a given unit of time, and its SI units are meters per second (m/s).
instantaneous speed
the speed of an object at one instant of time. The instantaneous speed of an object will always be equal to the magnitude of the object's instantaneous velocity, which is the measure of the average velocity as the change in time approaches zero. v = instantaneous velocity delta x = change in position delta t = change in time
Kinematics
the study of how things move DISPLACEMENT, VELOCITY, and ACCELERATION.
Find the X and Y components of the following vector: V = 10 m/s Theta = 30 degrees
X = 5 root 3 m/s Y = 5 m/s
What does the CGS unit system stand for?
centimeter, gram, second
What is the SI unit for time?
seconds (s)
At the atomic scale: length can be given in what 2 ways? ex. for wavelengths
1. 1 angstrom = 10^-10 m 2. nanometers: 1 nm = 10^-9 m
What are the steps to finding a Resultant (R) vector? How do you find the MAGNITUDE of the Resultant vector? How do you find the DIRECTION (theta) of the Resultant vector?
1. Separate the vectors into their X and Y components. 2. Add all the x-components of each vector to one another to the X-component of R. Add all the y-components together to get the Y-component of R. 3. Find the magnitude of the Resultant vector using PYTHAGOREAN THEOREM. R = the square root of (Rx^2 + Ry^2) 4. Find the DIRECTION (THETA/ANGLE) of the resultant using the relationship Theta = TAN INVERSE (Ry / Rx)
What happens when you multiply vectors by other vectors?
1. You can multiply TWO vectors to create a SCALAR QUANTITY (like WORK). 2. You can multiply TWO vectors to create a THIRD VECTOR (like torque).
How do positive or negative exponents of 10^x impact size?
10^-x, the exponent is NEGATIVE = SMALL 10^x, the exponent is POSITIVE = LARGE The greater the negative exponent, the smaller the measurement is. ex. 10^-35 meters. The greater the positive exponent, the larger the measurement is. ex. 10^26 meters.
Vector Dot Product
A form of vector multiplication, where two vectors are multiplied to produce a scalar. The dot product of two vectors, A and B, is expressed by the equation A · B = AB cos (angle between the 2 vectors).
Vectors and scalars both have a magnitude/size, but what distinguishes a scalar from a vector?
A scalar does NOT have a direction, while vectors have BOTH magnitude/size AND a direction.
vector components
A vector (e.g. Force) separated into vertical and horizontal components
Ex. In one year, Earth travels roughly 940 million km, but its DISPLACEMENT is zero. d (distance) = 9.4 x 10^8 km x (displacement) = 0 km
Average SPEED of Earth: (9.4 x 10^8) km/ (3.16 x 10^7) s = 29.8 km/s Average VELOCITY of Earth: 0 km/ (3.16 x 10^7) s = 0 km/s
Acceleration
Change in velocity divided by the time it takes for the change to occur. m/s^2
Displacement
Distance and direction of an object's change in position from the starting point. Displacement = (final distance - initial distance)
Distance vs. Displacement
Distance is a scalar quantity that refers to "how much ground an object has covered" during its motion. Displacement is a vector quantity that refers to "how far out of place an object is"; it is the object's overall change in position.
At the atomic scale: energy can be expressed in?
Electron-volts: 1 eV = 1.6 x 10^-19 J
True or False: If C = A x B, where A is directed towards the RIGHT side of the page and B is directed to the TOP of the page, then C is directed mid-way between A and B at a 45 degree angle.
FALSE. This would only work for ADDING vectors. When MULTIPLYING vectors, you must use the RIGHT HAND RULE. C points OUT of the page.
What are the steps of vector subtraction? Which vector (positive or negative) do you flip to add to the other positive vector?
Flip the negative vector and add head to tail to the positive one; resultant vector is head to head. A - B = A + (-B), where B represents a vector with the SAME magnitude as B, but pointing in the OPPOSITE DIRECTION. Vector subtraction may also be performed on the component vectors first and then combined to create the final vector.
If the newton is the product of kg and meters/second^2, what units comprise the pound?
Force = mass * acceleration mass = kg and acceleration = m/s^2 1 pound = 1 (slug*ft)/s^2 mass = slug (lb*s^2)/ft acceleration = ft/s^2
Force equation
Force = mass x acceleration 1 Newton = (kg*m)/s^2
BOLD face = vector quantity Italics = scalar quantity
In Kaplan books.
What is the relationship between instantaneous velocity and instantaneous speed? Between average velocity and average speed?
Instantaneous speed is the MAGNITUDE of the instantaneous velocity vector. Average speed and average velocity may be UNrelated because speed does NOT depend on displacement, but is rather the total DISTANCE travel divided by time.
What does SI unit system stand for?
International System of Units
A block moved a distance of 5m and distance is a scalar quantity. If a block is moved 5m to the right, what type of quantity is it?
It is a VECTOR quantity. Displacement is the vector quantity of distance (scalar quantity).
What happens to a vector when it is multiplied by a scalar?
Its MAGNITUDE will change. If vector A is multiplied by scalar n, the new vector will be B. (B = nA). MAGNITUDE of B = vector A * ABSOLUTE VALUE of n DIRECTION of B = look at the sign on n (scalar). - If sign is POS, A and B are in the SAME direction. - If sign is NEG, A and B point in the OPPOSITE direction.
What is the derived SI unit for Work and Energy?
Joule (kg*m^2)/s^2
What is the SI unit for temperature?
Kelvin (K)
Vector Cross Product
Magnitude of A * Magnitude of B * sine (angle between them).
What are the magnitudes and directions of the resultant vectors from the following cross products: C = AxB and D = BxA A: X = -3, Y = 0 B: X = 0, Y = +4m
Magnitude of Vector A: 3 Magnitude of Vector B: 4 Angle between them: 90 degrees (because one is oriented in the x-direction and the other is in the y-direction, the angle between them is 90). Cross Product = 3 x 4 x sin90 = 3*4*1 = 12 N*m Magnitude of the THIRD vector = 12 N*m Vector C = 12 N*m pointing INTO the page Vector D = 12 N*m pointing OUT of the page
When calculating the sum of vectors A and B (A+B) we put the tail of B at the tip of A. What would be the effect of reversing this order (B+A)?
NO difference between the two resultants when ADDING two positive vectors.
The resultant of a cross product will always be ______________ to the plane created by the 2 vectors.
PERPENDICULAR Because the MCAT is a 2D test, this usually means that the vector of interest will be going INTO or OUT of the page (or screen).
Speed
Rate of the actual distance an object travels per unit of time.
Distance, speed, energy, pressure, and mass are all what type of quantities?
SCALAR quantities
Dot Product produces a ______. Cross Product produces a ______.
Scalar (uses COS of theta) Vector (uses SINE of theta)
True or False: Total DISTANCE traveled can never be less than total DISPLACEMENT.
TRUE. Distance will ALWAYS be equal or larger than displacement.
A block moves a distance of 5m and the change in time is 2 seconds. How fast is the block going?
The block moved 5 meters in 2 seconds. 5m/2s = 2.5 m/s. The SCALAR quantity for how FAST something is going is SPEED.
A block moved 5m to the right in 2 seconds. How fast is the block going in the right direction?
The magnitude of the speed is 5m/2s = 2.5 m/s to the right. DIRECTION and SPEED are indicated. This is a VECTOR quantity for how fast the block is moving and that vector quantity is VELOCITY.
average speed
The overall rate of speed at which an object moves; calculated by dividing the total DISTANCE an object travels by the total time.
average velocity
The total DISPLACEMENT divided by the time interval during which the displacement occurred
The ANGLE of the resultant vector can be calculated by knowing INVERSE TRIG functions.
Theta = tan^-1 (Y/x) Angle = TAN INVERSE of (OPP/ADJ)
How do you generate a scalar quantity using vector multiplication? (ex. Work)
To generate a scalar quantity (work), multiply the MAGNITUDES of two vectors of interest (ex. force * displacement) and the COSINE of the angle BETWEEN the two vectors. This is called a DOT PRODUCT (A*B)
What is the magnitude of the vector with the following components? X = 3 m/s Y = 4 m/s
V = 5 m/s
Displacement, velocity, acceleration, and force are all what type of quantity?
VECTOR quantities
When calculating the difference of vectors A and B (A-B) we invert B and put the tail of this new vector at the tip of A. What would be the effect of reversing this order (B-A)?
Vector A would instead need to be inverted. The resultant vector of A-B would have the SAME MAGNITUDE as B-A, but its direction/orientation would be in the OPPOSITE direction.
Provide a definition for DISPLACEMENT or VELOCITY in terms of the other variable.
Velocity = rate of change of the DISPLACEMENT of an object over time. Displacement = a function of velocity acting over a period of time.
What is the derived SI unit for Power?
Watt (kg*m^2)/s^3 Watt = J/s = (N*m)/s = (kg*m^2)/s^3
How do you generate a third vector using vector multiplication? (ex. Torque)
You need to determine both its magnitude and direction. Multiply the MAGNITUDES of the two vectors of interest (force and lever arm) and the SINE of the angle BETWEEN the two vectors. Once we have the magnitude, use THE RIGHT HAND RULE to determine its direction. This is called the CROSS PRODUCT (A x B).
What is the displacement of a man who walks 2 km east, then 2 km north, then 2 km west, then 2 km south?
ZERO. Total distance traveled is 8 km. However, his change in position (displacement) is 0 km, because he ends up in the same place he started.
Unit Circle
a circle with a radius of 1
Tip to tail method
a method for finding a resultant vector in which the tail of one vector is drawn from the tip of another vector
Order the following units from smallest to largest: centimeter, angstrom, inch, mile, foot
angstrom < centimeter < inch < foot < mile
Pythagorean Theorem To find the magnitude of the Vector (hypotenuse) PT can be used.
a²+b²=c² V = the SQUARE ROOT of (a^2 + b^2)
