Summarizing Centripetal Force

Summary

• Centripetal force \({\text{F}}_{\text{c}}\) is any force causing uniform circular motion. It is a “center-seeking” force that always points toward the center of rotation. It is perpendicular to linear velocity \(v\) and has magnitude
  \(\phantom{\rule{0.25em}{0ex}}{F}_{\text{c}}={\text{ma}}_{\text{c}}\text{,}\)

  which can also be expressed as

  \(\left. \begin{array}{c} {F}_{\text{c}}=m\cfrac{{v}^{2}}{r}\\ \text{or}\\ {F}_{\text{c}}=\text{mr}\omega^{2}\end{array}, \right\}\)

Glossary

centripetal force

any net force causing uniform circular motion

ideal banking

the sloping of a curve in a road, where the angle of the slope allows the vehicle to negotiate the curve at a certain speed without the aid of friction between the tires and the road; the net external force on the vehicle equals the horizontal centripetal force in the absence of friction

ideal speed

the maximum safe speed at which a vehicle can turn on a curve without the aid of friction between the tire and the road

ideal angle

the angle at which a car can turn safely on a steep curve, which is in proportion to the ideal speed

banked curve

the curve in a road that is sloping in a manner that helps a vehicle negotiate the curve