Question

http://www.mit.edu/~8.01/quiz94/fip8l94.html
http://www.mit.edu/~8.01/quiz94/fisbl94.html

An Eskimo child is using his parents' hemispherical igloo of radius R as a chute. He starts off from rest at the top and slides down under the influence of gravity. The surface of the igloo is effectively frictionless. Derive an expression for the angle theta (with respect to the vertical) at which the child loses contact with the igloo.

Can someone please explain the conditions in which the child would start losing contact? I don't understand the first equation (1) in the solution. Thank you!!

Answer 1

In order to continue traveling in circular motion (I.e. be in contact with the igloo) there has to be enough force to maintain centripetal acceleration. when the speed of the eskimo becomes too great, the normal force will not be enough to pull him against the outside of the igloo. I 'm not sure I understand the first equation in that solution either though