How can a circular motion be explained?
Circular motion explained + example tasks with solution (physics)
In the following we want to deal with the circular motion. We divide this text into different sections.
- Frequency & duration
- Track speed
- Angular velocity
- Centripetal acceleration
- Centripetal Force & Centrifugal Force
- Example tasks with solutions
So let's get started! ;)
Frequency & duration
Let's start with the period of rotation. The period of revolution is what the name also says, it indicates the time t that is needed for one revolution. The period of circulation is formalized with the capital letter Are defined. The associated unit is (Second).
Now we come to the frequency. The frequency, crudely speaking, indicates the revolutions per second. We use the letter for the frequency a.
Expressed formally, the following applies to the frequency: with the unit or .
Now we can also derive the relationship to the period of rotation. If we to dissolve, we get . We now also have a formula for the period of rotation.
In the uniform motion, the speed is defined as .
Now with a circular path the segment is the circumference of a circle. The perimeter of a circle is defined as . So we bet for the scope a.
Since we are talking about a revolution, we can for the time also the period of circulation deploy. So we get:
We have now derived a formula for the orbital velocity. Since we know that is defined, we can also rewrite to
We now have two equations for the orbital velocity.
The speed in the uniform motion is defined as . Since we do not cover a “straight” distance in the circular movement, but an angle, we can write .
Since we have to calculate e.g. are not allowed to use an angle, we have to convert from degrees to radians. This conversion is very easy to do if you know that corresponds to.
So if we want to go around a whole circuit, we can also use the counter write. In concrete terms: .
Well we can for the time also the period of circulation start because we are now doing a complete circling.
We can still rewrite this expression (da applies) to
In physics, the speed is now by the Greek letter (Omega) replaced. We therefore get for the angular velocity
with the unit
We now take up the path speed again and can now derive another formula for the path speed.
The equation for the path speed is:
We see that there shows up as a product. Now that we know that also the same we can exchange this expression and get another notation for the path speed
The centripetal acceleration can be derived from a right triangle. One cathetus corresponds to this and the hypotenuse is . (The r comes from the extra radius.)
Now, according to the Pythagorean theorem:
We now use the letter instead of the cathetus for radius.
After resolving the brackets we get:
Now we still have to carry out a border crossing since the formula only applies if is pretty small. We know the term Limes from mathematics. We want to use it here as well.
We solve up and get for the centripetal acceleration
Centripetal Force & Centrifugal Force
We know the force is defined as . Since we are watching the centripetal acceleration we can now use the acceleration exchange and we get for the centripetal force:
The centripetal force is defined exactly like the centripetal force. .
Example tasks with solutions
1. Example task
A body moves on a circular path with the radius . It has the constant orbit speed of .
a) What is the angular velocity of the body?
b) What is the centripetal acceleration?
For task a: We first write out the information.
Now let's use the formula and adjust around.
So we get:
Answer: The body has an angular velocity of .
For exercise b: We write out the details again.
and acceleration is sought.
We take the formula and insert the information.
Answer: The body has a centripetal acceleration of .
2. Sample task
The moon movement can be approximated as a uniform circular movement with the radius of the orbit to be viewed as. The orbital time of the moon around the earth is 27 days, 7 hours and 43 minutes.
a) What is the orbit speed of the moon?
b) Which centripetal acceleration acts on the moon?
To a: First we write out the information.
Now let's use the formula and set in.
Answer: The moon has an orbital speed of .
To b: We write out the details again.
We now use the formula and set in.
Answer: A centripetal acceleration of .
Have fun recalculating the sample exercises with the solution!
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