A student has 65cm long arms. What is the minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any?

angular-velocity

#1

A student has 65cm long arms. What is the minimum angular velocity (in rpm) for swinging a bucket of water in a vertical circle without spilling any? The distance from the handle to the bottom of the bucket is 35cm.

Answer:

Ok so what you are really asking for is the critical speed. You could derive the equation by using the typical ΣF=ma notice that at the bottom normal force is against the force of gravity and at the top normal force works with gravity. But to save you the trouble the critical speed is rg−−√