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Example scenarios

In this section, I will work through some examples that illustrate what you learned in the earlier section along with what you have learned in earlier modules.

Circumference of the Earth at the equator

The radius of the Earth at the equator is equal to approximately 6378km. What is the circumference of the earth at the equator.

Solution:

If you were to travel around the Earth at the equator, you would travel along a circular arc that subtends an angle of 2*pi radians. We know how to computethe length of the circular arc given the radius and the subtended angle:

arc length = (subtended angle) * radius, or

circumference = 2*pi*6378km = 40074 km

Speed of a point on the equator

The Earth rotates around its axis once each 24 hours. Therefore, a point on the equator makes one full trip around a circle with the circumference of theEarth each 24 hours.

Assume you are standing at a point on the equator. Ignoring all of the other motions of the universe, what is the speed with which you are traveling aroundthat circle?

What is the angular velocity of the earth in radians per second.

Does the angular velocity of the Earth change when you drive North from the equator?

Solution A

Speed

Since we already know the circumference of the Earth, we know that you will travel 40074 km each 24 hours. Therefore,

speed = 40074km/24hr = 463.8 meters/second, or

speed = 1037 miles/hour

Did you know that you are constantly moving through space at a speed slightly greater than 1000 miles per hour?

Angular velocity

We also know that the earth rotates around its axis by 2*pi radians each 24 hours. Therefore, the angular velocity of the earth is

w = 2*pi radians/24 hours = 7.27 *10^(-5) radians / second

Differences in angular velocity

For purposes of this discussion, the Earth does not distort as it rotates. Therefore, the angular velocity of every point on the surface of the Earthrotates around the Earth's axis with the same angular velocity; namely 2*pi radians every 24 hours.

However I did see on TV the other day that the angular velocity of the Earth's core may be different from the angular velocity of the outer crust ofthe Earth. Apparently this can happen because the core is not firmly attached to the crust, but rather is suspended in a bath of molten rock.

Solution B

You learned earlier that the speed is equal to the product of the angular velocity and the radius. Therefore,

speed = w * r, or

speed = (7.27 *10^(-5) radians / second) * 6378km, or

speed = 463.7 m/s

which agrees with Solution A above.

Note that w represents angular velocity and r represents radius in the above calculations.

Period and frequency

A child's toy contains a round disk that rotates with a period of 0.628 seconds.

What is the frequency with which a spot on the edge of the disk passes a fixed mark on the body of the toy.

What is the angular velocity of the toy?

Solution:

f = 1/T = 1/(0.628) = 1.59 Hz

w = 2*pi*f = 10 radian/second

where

  • f represents frequency
  • T represents the period
  • w represents angular velocity

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
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John Reply
what is physics
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Can you compute that for me. Ty
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what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
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Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
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Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
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"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
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answer
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progressive wave
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Mohammed
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Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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