Centripetal Force

Any motion in a curved path represents accelerated motion, and requires a force directed toward the center of curvature of the path. This force is called the centripetal force which means "center seeking" force. The force has the magnitude

Swinging a mass on a string requires string tension, and the mass will travel off in a tangential straight line if the string breaks.

The centripetal acceleration can be derived for the case of circular motion since the curved path at any point can be extended to a circle.

Note that the centripetal force is proportional to the square of the velocity, implying that a doubling of speed will require four times the centripetal force to keep the motion in a circle. If the centripetal force must be provided by friction alone on a curve, an increase in speed could lead to an unexpected skid if friction is insufficient. Calculation 计算 注意，向心力与速度的平方成正比，这意味着速度加倍将需要四倍的向心力以保持圆周运动。如果曲率半径上的向心力仅由摩擦力提供，速度的增加可能导致滑移，如果摩擦力不足的话。

Centripetal Force Calculation

Note that the conditions here assume no additional forces, like a horizontal circle on a frictionless surface. For a vertical circle, the speed and tension must vary. 请注意，此处的条件假设没有额外的力，例如在无摩擦表面上的水平圆周运动。对于垂直圆周运动，速度和张力必须变化。

Any of the data values may be changed. When finished with data entry, click on the quantity you wish to calculate in the formula above. Unit conversions will be carried out as you enter data, but values will not be forced to be consistent until you click on the desired quantity. Calculation for: Radius r = m = ft Mass = m=kg = slugs Weight = W=N = lbs Velocity = v=m/s = ft/s or in common highway speed units, velocity = km/h = mi/h Centripetal force= F=N = lbs 任何数据值都可以更改。完成数据输入后，点击公式上方你希望计算的量。在输入数据时会进行单位转换，但直到你点击所需的量时，值才不会被强制保持一致。计算：半径 r = m = ft 质量 = m = kg = slugs 重量 = W = N = lbs 速度 = v = m/s = ft/s 或常用高速公路速度单位，速度 = km/h = mi/h 向心力= F = N = lbs 中文译文中的待填/计算数值依次对应：1：r 2：rc 3：m 4：mc 5：w 6：wc 7：v 8：vc 9：vk 10：vm 11：f 12：fc。实际数值以上方原输入框为准。 Discussion of concept 概念讨论

Centripetal Acceleration

The centripetal acceleration expression is obtained from analysis of constant speed circular motion by the use of similar triangles. From the ratio of the sides of the triangles: