Finding the Optimal Radius for Keeping a Body on a Spinning Carousel

AI Thread Summary
To determine the optimal radius for a body on a spinning carousel with an angular velocity of 1.4 rad/s and a static friction coefficient of 0.2, the centripetal force must be balanced by the frictional force. The equation for centripetal force (F_c = mv^2/r) must equal the maximum static friction (F_f = μmg), leading to the relationship μmg = mv^2/r. The velocity can be expressed as v = ωr, allowing for substitution into the friction equation. The solution involves finding the radius r that satisfies these conditions, emphasizing the role of friction in preventing the body from slipping off the carousel. Understanding the forces at play is crucial for solving the problem accurately.
dannee
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Homework Statement



Carousel is spinning when w = 1.4rad / s.

on the carousel there is a given body.

Static friction between the carousel with the body is 0.2

What is the radius that you can put the body on the carousel that the body won't slip?

Homework Equations





The Attempt at a Solution



i've tried to solve it by calculating maximum friction without that body moves while accelerating is 0.

forces on the body is (f=ma=0) 2mwv-0.2*mg, which leads to w=1/v

v=w*r means that r=v^2=1/(1.4)^2

but this answer is wrong. can someone help and tell me what I'm missing?
 
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Try thinking: what is the effect of the friction on the body? How does the body spins (that is, which FORCE is responsible for its spinning)?
 
the body has circular acceleration, but again, i don't see how it's related to the movement on carousel through the sideline of the carousel.
 
dannee said:
the body has circular acceleration, but again, i don't see how it's related to the movement on carousel through the sideline of the carousel.
The body isn't moving with respect to the carousel. There's no coriolis force here.

What's the only force acting on the body to produce its centripetal acceleration?
 

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