# DYNAMICS: SPINNING CONE WITH MASS TIME SENSITIVE (30 mins)

## Homework Statement

Dynamics Problem: Spinning cone with mass!?

The sides of a cone make an angle "THETA" with the vertical. A small mass "m" is placed on the inside of the cone and the cone, with its point down, is revolved at a frequency "f" about its symmetry axis. If the coefficient of static friction is "MU", at what positions on the cone can the mass be placed without sliding on the code? (Give the maximum and minimum distances, "r", from the axis)

## Homework Equations

I guess what it boils down to is what forces are acting on the mass... what am I missing. So far I have these forces:
Centripetal, friction, and gravity. Is that it? And is (f/(2*pi*r)) equal to velocity?

## The Attempt at a Solution

set up two equations, set normal force equal to each other, and solve for r?

(F_n)*cos(THETA) = (F_centrip) - (F_friction)*sin(THETA)
m*g = (F_n)*sin(THETA) + (F_friction)*cos(THETA)

i'm missing something :( what is it?!-

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1. Centripetal force is a name given to the net force that points towards the center of the circular motion, i.e. it is not an individual impetus of force.
2. The mass is touching the cone, right. If a book is sitting on a horizontal table, i.e. touching the table, what forces act on the book?

gravity, normal

Ah, so a normal force acts on the book since it is in contact with the table. How about your mass?

gravity, normal, friction? and normal is different because it's spinning?

What do you mean different? To determine forces, I go through a list in my head- are there strings attached?- tension/ is anyone pushing?- applied force/is this object in contact with something?-normal force/ etc.
After that draw a free body diagram.

k got it thanks