Centripetal Force on Body in Circular Path

Theorem

Let $B$ be a body of mass $m$ constrained to move at constant speed $v$ in a circular path $C$.

Let $\mathbf F$ denote the centripetal force on $B$.

$(1): \quad$ The direction of $\mathbf F$ is towards the center of $C$

$(2): \quad$ The magnitude of $\mathbf F$ is given by:

$\size {\mathbf F} = \dfrac {m v^2} r$

or:

$\size {\mathbf F} = m r \omega^2$

where $\omega$ denotes the angular speed of $B$.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): centripetal force
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): circular motion
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): centripetal force
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): circular motion