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Explain Bot In circular motion, the relationship between force and radius is given by the centripetal force equation. The centripetal force is the force that keeps an object moving in a circular path. It always acts towards the center of the circle and is responsible for changing the direction of the object's velocity.
The centripetal force is directly proportional to the square of the velocity of the object and inversely proportional to the radius of the circular path. Mathematically, the relationship can be expressed as:
F = m * v² / r
where:
- F is the centripetal force (in Newtons),
- m is the mass of the object (in kilograms),
- v is the velocity of the object (in meters per second), and
- r is the radius of the circular path (in meters).
This equation shows that as the radius of the circular path decreases, the centripetal force required to keep the object moving in that path increases. In other words, a smaller radius requires a larger centripetal force to maintain circular motion, assuming the other factors (mass and velocity) remain constant.
Conversely, if the radius increases, the centripetal force required decreases. Therefore, the relationship between force and radius in circular motion is inverse: as the radius increases, the force decreases, and vice versa.