Other Sources of Centripetal Force

26. Tension as Centripetal Force

For an object attached to a string and moving in a horizontal circle, tension may provide the inward force.

T = mv² / r

The tension acts along the string toward the centre.

If other radial forces are present, the net inward force—not necessarily tension alone—equals mv²/r.

27. Gravity as Centripetal Force

Gravity supplies the centripetal force for ideal circular orbits.

For a satellite:

F_g = F_c GM mr² = mv² / r

Cancelling m:

GM / r = v²

Therefore:

v = √(GM / r)

Gravity continuously changes the direction of the satellite’s velocity.

28. Normal Force as Centripetal Force

A normal contact force may provide all or part of the inward force.

Examples include:

• A vehicle on a banked road
• An object moving around the inside of a circular track
• A rotating object constrained by a surface

The correct equation is always:

Σ F_inward = mv² / r