Chapter 17
Ten Online Problem-Solving Tools
In This Chapter
Using online calculators
Finding energy, reactance, frequency, half-life, and more
Physics requires a lot of number crunching, and you can find help for that online. Many specialized physics calculators are available, and this chapter takes a look at some of the best. Just plug in your numbers, and the calculator can add your vectors, calculate frequency and wavelength, and even give you some quick numbers on relativity or radioactive decay.
Vector Addition Calculator
Vector addition can be very time-consuming. What’s the direction of the net force from three charges on a test charge? What’s the force’s magnitude?
Now you can get some help with the vector addition calculator. Just enter the magnitude and direction (in degrees) of up to ten vectors, click the Calculate button, and you’re there — the vector sum is displayed in two text boxes: One holds the vector sum’s magnitude, and the other holds its direction. Simple.
You can find the vector addition calculator at
Centripetal Acceleration (Circular Motion) Calculator
If you have an electron orbiting in a magnetic field (see Chapter 4), you can calculate its centripetal acceleration using a lot of math — or you can let the centripetal acceleration calculator do it for you.
Select what you want to calculate — centripetal acceleration, radius, or velocity — from a drop-down box and then enter the other two values. The calculator does the rest.
You can find the centripetal acceleration calculator at
easycalculation.com/physics/classical-physics/centripetal-acceleration.php
Energy Stored in a Capacitor Calculator
This calculator gives you the energy stored in a capacitor. You enter the capacitance in farads and the charge in coulombs; then click the Calculate button. The calculator displays the stored energy in the capacitor in joules.
You can find this calculator at
easycalculation.com/physics/electromagnetism/stored-energy-electrical.php
Electrical Resonance Frequency Calculator
When you have a circuit with an inductor, a capacitor, and a voltage source that alternates at a given frequency, you can have resonance if you tune the frequency just right — that is, you can find a frequency that maximizes current in the circuit because the inductive reactance and the capacitive reactance cancel each other out (see Chapter 5 for details).
Now you can use an online calculator to find the resonance frequency of a circuit. You can also solve for the capacitance needed for resonance (given a voltage source frequency and an inductance), or you can solve for the needed inductance (given a voltage source frequency and a capacitance).
Just click the button indicating what you want to solve for — resonance frequency, capacitance, or inductance — click buttons to indicate which units you’re using for each measurement (for instance, click either Henrys or MilliHenrys for inductance), enter the two numbers you know, and click the Calculate button; the number you want to solve for is displayed. Cool.
You can find the resonance frequency calculator at
Capacitive Reactance Calculator
This calculator lets you figure the capacitive reactance of a capacitor, given a certain capacitance and a frequency. Just enter the two values and click the Calculate button, and you’re done.
You can find this calculator at
easycalculation.com/physics/electromagnetism/capacitive-reactance.php
Inductive Reactance Calculator
This calculator lets you calculate the inductive reactance of an inductor. You enter the inductance values and the frequency of the voltage source, click the Calculate button, and presto! The inductive reactance appears in a text box.
This calculator is at
easycalculation.com/physics/electromagnetism/inductive-reactance.php
Frequency and Wavelength Calculator
This calculator lets you convert from frequency to wavelength or wavelength to frequency for light. Just enter a value in the Input box and click one of the buttons:
Buttons if you know wavelength: cm, feet, meters
Buttons if you know frequency: Hz, KHz, MHz
The calculator displays the corresponding value — for example, if you enter a value and click Hz, the calculator takes the value you entered as a frequency in hertz and displays the corresponding wavelength.
This calculator is at
Length Contraction Calculator
When you have speeds near the speed of light, you get length contraction. You can figure out what the length contraction is with the length contraction calculator. Just enter the fraction of the speed of light you’re going (as a decimal) and click the second box. The length contraction factor appears in that box. Simple.
Find this calculator at
hyperphysics.phy-astr.gsu.edu/hbase/relativ/tdil.html
You can check out Chapter 12 for more info on length contraction and Einstein’s theory of special relativity.
Relativity Calculator
The online relativity calculator specializes in calculations involving the relativity factor:
The calculator changes units and solves for velocity or the relativity factor as you like. You enter a value in the Input box and then click one of these buttons:
Miles/second: The calculator finds the relativity factor.
Kilometers/second: The calculator finds the relativity factor.
c = 1: The calculator finds the relativity factor using your input as a fraction of c.
Factor of change: The calculator finds the speed needed to give you the input relativity factor.
You can find the relativity calculator at
Half-Life Calculator
Working with radioactive decay is always a little tricky. Given a beginning amount of material and a half-life, how much material is left after a certain time? (Half-life is the time required for the amount of radioactive material to reduce by half through radioactive decay — see Chapter 15 for details.)
You can use the half-life calculator to find out. Click a button depending on what you want to solve for:
Time (years)
Half-life (years)
Beginning amount (grams)
Ending amount (grams)
Then enter the numbers as prompted. You can find the half-life calculator at