Tru Physics

Centripetal Force

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Tru Physics
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Centripetal force is the force that is necessary to keep an object moving in a circular path. When an object is moving in a circle, it is constantly changing direction, which means it is also constantly accelerating. Centripetal force is the force that causes this acceleration. This is required by Newton’s Second Law:

\sum \vec{F} = m \vec{a}

or, in this case:

\vec{F}_c = m \vec{a}_c

where F_c is the centripetal force, m is the mass, and a_c is the centripetal acceleration.

Definition of Centripetal Force

The centripetal force is the net force acting on an object that causes it to move in a circular path. The word “centripetal” comes from the Latin words “centrum” meaning center and “petere” meaning to seek. Therefore, centripetal force can be thought of as the force that seeks the center of the circle.

Formula for Centripetal Force

In the case of uniform circular motion, acceleration is equal to the square of the velocity divided by the radius of the circle:

a_c = \dfrac{v^2}{r}

Therefore, the formula for centripetal force is:

F_c = m \dfrac{v^2}{r}

where F_c is the magnitude of the centripetal force, m is the mass of the object, v is the velocity of the object, and r is the radius of the circle.

Note that we did not write the vector form of \vec{F}_c in the equation above. This is because the direction is constantly changing. However, the direction of \vec{F}_c is understood intuitively to point directly toward the center of the circular motion.

Examples and Applications

Some common examples of centripetal force include the motion of planets around the sun, the motion of cars around a curve in a road, and the motion of a ball attached to a string being swung around in a circle.

Centripetal force is used in many applications, including amusement park rides such as the Ferris wheel and the roller coaster, as well as in the design of circular motion machines such as centrifuges and washing machines. It is also used in the study of celestial mechanics to describe the motion of planets and other objects in space.

Centrifugal Force

It’s important not to confuse the centripetal force with the centrifugal force. Note that the centrifugal force is not a “real” force in the usual sense of the term, but rather a “fictitious” force that appears to act on an object moving in a circular path. The centrifugal force is the apparent outward force that appears to be acting on an object in circular motion. In reality, this force is the result of inertia and the lack of a centripetal force acting on the object in the opposite direction.

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