Question

Problem 3.18 A small ball A of mass mis con- nected to a vertical shaft at O by a string of length I. The system is initially at rest, with the pendulum in contact with the shaft. The shaft is then slowly set in rotation to reach a constant angular velocity w. Neglect the size of the balls and the diameter of the shaft, that is, O is on the axis of the shaft. a. Show that the line OA describes a cone of half-angle only if w exceeds a minimum - value w1. Find angle ♡ as a function of W. What happens if w<w? b. The string is known to break if its tension - reaches the value 20mg. Find the value wy of ? angular velocity w when the string breaks.

Answer 1

it sotutes at half cone angle 6. Solution FBD of ball when Equillibrium EH-O Tsing = mwer Toina = mw2 esine T= mwil Ev=0 TOOS 6 = mg - putting in @ mwl cs6 = mg coso = 2 where = e sing value 1 tot 1 so of cost is between Os 31 angle with rol - if wew, than mass will not make any When T= 20mg from equation ④ "Ta mwed Song - Mw 'a W 2 909