Physics 1 (1/15) - Vectors
What are the four rules for significant digits?
1. Any digits between zeroes on the left and right are significant. Ex. 000.345000 (345 is significant) 2. Zeroes to the right of the last nonzero digit are significant only if there is a decimal point in the number (trailing zeroes). Ex. 3490.0 and 1.10 is all significant but in 3490 only 349 is significant. 3. Zeroes to the left of the first nonzero digit (non-leading zeroes) are not significant. Ex. .0000345 (345 is significant only) 4. For measurements, the last digit (an estimation) is not considered significant.
What is the unit of measurement and symbol for each of these? 1. Length 2. Mass 3. Time 4. Current 5. Amount of Substance 6. Temperature 7. Luminous Intensity 8. Force 9. Word and Energy 10. Power
1. Meter (m) 2. Kilogram (kg) 3. Second (s) 4. Ampere - Coulomb/second (A) 5. Mole (mol) 6. Kelvin (K) 7. Candela (cd) 8. Newton (kg*m/S^2) 9. Joule (kg*m^2/S^2) 10. Watt (kg*m^2/S^3)
How do we multiply two vectors to get a Vector quantity?
1. We use the Cross Product Method to find the magnitude first. Sometimes the angle must be inferred from the problem. 2. Then we use the Right-hand rule to find the direction of the resultant vector
What is the square root of these common numbers? 2 3 5
1.4 1.7 2.2
Convert 1 electron-volt (eV) to Joules
1.602x10^-19 J
Convert 1 atomic mass unit (amu) to kg
1.661 x 10^-27 kg
Convert 1 Cal to cal
1000 calories
If meters is the base (10^0), then what is deci?
10^-1 (d)
If meters is the base (10^0), then what is pico?
10^-12 (p)
If meters is the base (10^0), then what is centi?
10^-2 (c)
If meters is the base (10^0), then what is milli?
10^-3 (m)
If meters is the base (10^0), then what is micro?
10^-6 (u)
If meters is the base (10^0), then what is nano?
10^-9 (n)
If meters is the base (10^0), then what is deka?
10^1 (da)
If meters is the base (10^0), then what is tetra?
10^12 (G)
If meters is the base (10^0), then what is hecto?
10^2 (h)
If meters is the base (10^0), then what is kilo?
10^3 (k)
If meters is the base (10^0), then what is mega?
10^6 (M)
If meters is the base (10^0), then what is giga?
10^9 (G)
Convert: 1 foot to inches
12 inches
What are square roots of the following common numbers: 11 16 12 17 13 18 14 19 15 20
121 144 169 196 225 256 289 324 361 400
2.17 x 10^2 - Where is the significand?
2.17 (Also called the mantissa and coefficient)
Convert: 1 inch to centimeters
2.54 cm
Convert 1 L to ounces
33.8 ounces (oz.)
Convert 1 calorie to Joules
4.184 J
Convert 1 pound (lb) to newtons
4.45 N
Convert: 1 mile to feet
5280 Feet
How do we use the Right-hand rule?
After finding magnitude of the resultant vector we apply the right hand rule accordingly: 1. Whichever vector is written first in the multiplication problem, we use the thumb of the right hand to point in its direction - regardless of whether it is the X or Y coordinate. Whichever coordinate (X or Y) is given, we use our thumb to point in its direction. Plus (+) is upwards or rightwards and Negative (-) is downwards or leftwards. 2. Then we use our four fingers of the right hand to point in the direction of vector B. You may need to rotate your wrist to get the right configuration 3. The direction our palm faces, is the direction of the resultant vector (usually into or out of the page/screen) on MCAT
How do we subtract vectors?
By changing the direction of the subtracted vector and then following the procedures for vector addition (tail-to-tip or component)
What is the difference between common log and natural log? What is the equation between the two?
Common log is base-ten logarithms and natural log (log (e) or ln are based on Euler's number: 2.71
Conversion factor to Fahrenheit from Celsius?
F=(9/5)C + 32
Which one of the three are always commutative functions in vectors I. Vector Addition II. Vector Subtraction III. Vector Multiplication
I. Vector Addition Vector Subtract and Vector Multiplication are not always commutative (although multiplication can be commutative). Changing the order in which the vectors are subtracted or multiplied will keep the magnitude the same but will invert the direction. Ex. A-B does not equal B-A because in the latter the direction of the vector is inverted.
When rounding two numbers containing decimals, in which directions should each number go for multiplication and division?
In multiplication if one goes down, the other should go up and vice versa In division, both numbers should go in the same direction.
Define Instantaneous velocity and speed
Instantaneous Velocity is the limit of the change in displacement over time as the change in time approaches zero. Instantenous speed is simply the magnitude of the instantaenous velocity.
What is the relationship between instantaneous velocity and instantaneous speed?
Instantaneous velocity = Instantanous speed always
Conversion factor to Kelvin from Celsius?
K=C + 273
How do we determine significant digits when multiplying or dividing numbers? Adding or subtracting?
Round to the number of significant digits that is the same as the least number of significant digits in any of the factors, divisors, or dividends. When adding or subtracting the decimal point is maintained rather than maintaining significant figures.
What is the Sin, Cos, and Tan of the angle 0?
Sin 0 = 0 Cos 0 = 1 Tan 0 = 0
What is the Sin, Cos, and Tan of the angle 180?
Sin 180 = 0 Cos 180 = -1 Tan 180 = 0
What is the Sin, Cos, and Tan of the angle 30?
Sin 30 = 1/2 Cos 30 = (sq3)/2 = .866 Tan 30 = 0 = .577
What is the Sin, Cos, and Tan of the angle 45?
Sin 45 = (sq2)/2 = .707 Cos 45 = (sq2)/2 = .707 Tan 45 = 1
What is the Sin, Cos, and Tan of the angle 60?
Sin 60 = (sq3)/2 = .866 Cos 60 = 1/2 Tan 60 = (sq3) = 1.73
What is the Sin, Cos, and Tan of the angle 90?
Sin 90 = 1 Cos 90 = 0 Tan 90 = Undefined
What is the trend for Sin and Cos from 0-90 and do trigonometric functions apply to all triangles?
Sin increases from 0-90 and Cos decreases from 0-90 and trigonometric functions can apply to any triangle (not just right triangles)
How do we add multiple vectors in one dimension using the component method?
The component method involves breaking each vector into smaller component vectors that can give us an angle/degree within the problem. We can then use SOH CAH TOA to find the magnitude of sides and add those up to get a final resultant vector. We can also use the pythagorean theorem. We can also find the direction and angle (if we are given the magnitude of the vectors) of the vectors by using Sin-1, Cos-1, or Tan-1
Why is vector multiplication not commutative (unlike scalar multiplication)?
The magnitude aspect of vector multiplication is commutative but the direction aspect is not. The reason it is not commutative is because of the right-hand rule. Whichever vector is written first in the multiplication problem will indicate the starting point when applying the right hand rule. For example: C=A X B D=B X A A: X = -3 and Y = 0 B: X = 0 and Y = +4 The magnitude for both C and D is 12 but when applying the right-hand rule for C we start with -3 (pointing the thumb of our right hand leftwards first) but when applying the right-hand rule for D we start with +4 (pointing the thumb of our right hand upwards first)
What is the relationship between average velocity and average speed?
The two a different because avg. velocity is change in displacement/time Avg. speed is total distance travelled/time
True or false: Total distance traveled can never be less than total displacement
True: Total distance will always be equal to or more than the displacement
Vector x Scalar
Vector with a new magnitude that is parallel or antiparallel to its original direction. Ex. B=An (A and B are vectors and n is a scalar) 9=3(+3). Resultant vector is 9 and parallel to A -9=3(-3). Resultant vector is 9 and antiparallel to A
What are some common vector and scalar quantities?
Vector: 1. Displacement 2. Acceleration 3. Velocity 4. Force 5. Weight Scalar 1. Distance 2. Speed 3. Energy 4. Pressure 5. Mass
How do we multiply two vectors to get a scalar quantity?
We use the dot product method:
What is log1 and log10?
log1 = 0 log10=1