Swinging a Rock in a Circle

Swinging a Rock in a Circle#

Stewie watches as a rock tied to a string is swung clockwise in a vertical circle of radius \(r\). The string breaks when \(\theta\) = 0. Stewie observes that the rock reaches a maximum height \(h\) relative to the height of the centre of the circle. What is the angular speed \(\omega\) of the circular motion at the instant just before the string breaks?

For

Use

\(g\)

g

\(h\)

h

\(r\)

r
Stewie is seen swinging a rock on a string of length r, which is at an angle theta from horizontal. The rock reaches a height h once the string breaks.

Part 1#

Find an expression for \(\omega\) in terms of \(h\), \(r\), and the gravitational acceleration \(g\).

Answer Section#

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.