Is the Period of Centripetal Motion Proportional to the Radius?

In summary, the period of an object's revolution is directly proportional to its radius. This means that the period can be expressed as a multiple of the radius, with a constant factor. This relationship can be represented by a linear equation, where the period is equal to a constant multiplied by the radius. However, changes in the radius do not necessarily result in a change in the period.
  • #1
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How is the Period proportional to the Radius. (The Period being how long it takes for 1 full revolution of an object)

I am also assuming there is a tension force.
 
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  • #2
it looks the square of the period is proportional to the radius, rather.

centripetalforce.jpg
 
  • #3
That's what gets me stumped though =/.

The teacher says he is going to put in the test "Show that the radius is proportional to the Radius".

What does it mean to be proportional. (It means they have a relationship I guess) But what would you write down for an answer asking if something is proportional to something else.

If the radius is changed does the Period change?
 
  • #4
for a variable to be proportional to another, it implies a relationship of

A = kB (or B = pA)

where A and B are the related variables, and k or p is the constant depending on how you write the equation. thus they can be related as a straight linear line.

the radius does change when the period changes, but that is more of a statement like 'the radius increases when the period is longer', note that this statement does not really have any quantifiable mathematical relationship.
 

What is centripetal motion?

Centripetal motion is the motion of an object along a circular path, where the object experiences a force directed towards the center of the circle, known as the centripetal force.

What is the difference between centripetal force and centrifugal force?

Centripetal force is the force that keeps an object moving along a circular path, while centrifugal force is the apparent outward force experienced by an object in circular motion. Centrifugal force is a fictitious force and does not actually exist.

What is the role of centripetal force in circular motion?

Centripetal force is necessary to keep an object moving along a circular path. Without a centripetal force, the object would move in a straight line tangent to the circle.

What are some real-life examples of centripetal motion?

Some examples of centripetal motion include the orbit of planets around the sun, the motion of a car around a curved track, and the spinning motion of a roller coaster.

How is centripetal force related to Newton's laws of motion?

Centripetal force is a result of the application of Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In the case of circular motion, the force is directed towards the center of the circle, providing the necessary acceleration for the object to maintain its circular path.

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