Math

One exciting thing from math is the representation of real world in models, like algebraic symbols, graphs, etc.

Quantities in Math

Name	Symbol	Unit	Type
Area	A	m², meter²	scalar
base	b	m, meter	scalar
Circumference	C	m, meter	scalar
Height	h	m, meters	scalar
Radius	r	m, meters	scalar

Key Things to Know in Math

The angle is always measured from the normal line in waves questions.
All quantities have units, except coefficient of friction and index of refraction.
To use the physics formula, the unit for mass must be measured in kilogram, the unit for length must be measured in meters, the unit for time must be measured in seconds, the unit for work or energy must be measured in joules, the unit for power must be in watt.
The prefixes are power of ten multiplied to the unit.

Key Words in Math

direct relationship, linearly proportional relationship, inverse (indirect) relationship, magnitude

Direct relationship: when one variable increases, the other variable also increases.
Inverse relationship: When one variable increases, the other variable decreases.
Linear relationship: The ratio of one variable to the other variable is constant.
magnitude: the absolute value of a quantity.

Formula in Math

Area of a rectangle A = bh
Area of a circle = π r²
Circumferebce C = 2πr
c² = a² + b²
sin (θ) = \( \frac{a}{c} \)
cos (θ) = \( \frac{b}{c} \)
tan (θ) = \( \frac{a}{b} \)

Example 1

How many amperes (A) are in 130 milliamperes (mA)?

electrical current I = 130 mA × (10^-3 A / 1 mA) = 130 × 10^-3 A = 0.130 A

Example 2

Q: How do you convert 23 grams to kilograms?

m = 23 g × (1 kg / 10³ g) = 0.023 kg because k = 1 kilo = 10³

Example 3

Q: Show that on a ramp, the parallel component of force due to gravity is mg sin (θ).

Draw the F_g within the triangle-ramp. Draw an perpendicular dashed line from the arrow of the force due to gravity to the ramp surface.
You will be convinced that sin(θ) = F_g∥ ÷ F_g

Example 4

A cart travels 4.00 meters east and then 3.00 meters north. Determine the magnitude of the cart’s resultant displacement

Draw the vectors head to tail and draw the resultant from tail of first vector to the head of the second vector. c² = a² + b²; b = 4 m, a = 3m,
c = √(a² + b²) = √((3 m)² + (4 m)²) = 5 m

Exercises

1. A high-speed train in Japan travels a distance of 300. kilometers in 3.60 × 10³ seconds. What is the average speed of this train?
(1) 1.20 × 10^-2 m/s (3) 12.0 m/s
(2) 8.33 × 10^-2 m/s (4) 83.3 m/s

2. How many m/s are in 50 kilometers per hour?

3. How many m/s are in 60 miles per hour?