Understanding the Relationship between Force and Radius in Circular Motion

In summary, the two formulas for Fc are mathematically the same, but the first one shows that Fc is inversely proportional to r while the second one shows that r is directly proportional to Fc. This is because when the angular velocity (2pi/T) is constant, the velocity (v) is directly proportional to r. It should also be noted that the second formula is missing a factor of mass (m).
  • #1
Epsillon
70
1
Alright so in one formula Fc= mv^2/r and another Fc= 4pi^2r/T^2


Although the two formlas are the same Mathematicly but isn't Fc porportional to the inverse of the r as it is shown in the first one. So why is r directly porportional to Fc in the second one?
 
Physics news on Phys.org
  • #2
Epsillon said:
Alright so in one formula Fc= mv^2/r and another Fc= 4pi^2r/T^2Although the two formlas are the same Mathematicly but isn't Fc porportional to the inverse of the r as it is shown in the first one. So why is r directly porportional to Fc in the second one?

because if the angular velocity (2pi/T) is constant then v is directly proportional to r. Also, you are missing an m in your 2nd formula.
 
  • #3
No but isn't it supposed to be inversly proportional?
 
  • #4
Epsillon said:
No but isn't it supposed to be inversly proportional?

did you read what i wrote?
 
  • #5
Yes I understand this now thanks for the help :)
 

FAQ: Understanding the Relationship between Force and Radius in Circular Motion

What is circular motion relationship?

Circular motion relationship is a type of motion that occurs when an object moves in a circular path around a fixed point, known as the center of rotation. This type of motion is characterized by the constant distance between the object and the center of rotation, as well as the constant speed along the circular path.

What is the relationship between speed and radius in circular motion?

In circular motion, the speed of an object is directly proportional to the radius of the circular path it is moving in. This means that as the radius increases, the speed of the object also increases, and vice versa. This relationship is known as the tangential speed or linear speed.

How is angular velocity related to circular motion?

Angular velocity refers to the rate at which an object rotates around a fixed axis. In circular motion, the angular velocity is directly proportional to the tangential speed and inversely proportional to the radius of the circular path. This means that as the tangential speed increases, the angular velocity also increases, and as the radius increases, the angular velocity decreases.

What is the centripetal force in circular motion?

The centripetal force is the force that keeps an object moving in a circular path. In circular motion, this force is directed towards the center of rotation and is responsible for changing the direction of the object's velocity. The magnitude of the centripetal force is directly proportional to the mass of the object, the square of the tangential speed, and inversely proportional to the radius of the circular path.

How does centripetal force relate to centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences as it moves in a circular path. It is always directed towards the center of rotation and is directly proportional to the square of the tangential speed and inversely proportional to the radius of the circular path. This means that as the tangential speed increases, the centripetal acceleration also increases, and as the radius increases, the centripetal acceleration decreases.

Similar threads

Confused in diffferent forces involved in circular motion
Replies
7
Views
7K
Why Does Friction Provide Centripetal Acceleration in Circular Motion?
2
Replies
37
Views
3K
I The centripetal acceleration of the planets in our solar system
Replies
19
Views
3K
Tension in the thread: Centripetal Force in the Vertical plane
Replies
18
Views
8K
Centripetal Force vs Radius: Exploring Uniform Acceleration Lab Results
Replies
12
Views
5K
Motion of particle changing forces
Replies
3
Views
999
What happens when a car turns?
Replies
16
Views
1K
Can a Stone Remain in Circular Motion if Tension Equals Zero Before Velocity?
Replies
12
Views
3K
B Confusion while trying to build intuition of centripetal force
Replies
15
Views
3K
[Grade 12 Physics] Circular/gravitational motion
Replies
21
Views
2K

Hot Threads

Recent Insights

Back
Top