Motion in a plane II, Coin on a turntable with Vmax

[SherBear]

Homework Statement

A 3.90 g coin is placed 12.0cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of Ws= 0.800 and Wk= 0.410.

What is the maximum angular velocity with which the turntable can spin without the coin sliding?

Homework Equations

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The Attempt at a Solution

? no idea
can you please show all the steps and the solution, thank you!

 

[LawrenceC]

Draw a free body diagram of the coin showing all forces. Then look at the forces and determine how they interact with one another.

 

[SherBear]

Draw a free body diagram of the coin showing all forces. Then look at the forces and determine how they interact with one another.

Does a turntable turn clockwise? Normal force up, mg down, Ff opposite of the motion if clockwise then it's counterclock wise?

I have Vmax=SQRT Ws r g=SQRT .800*.12m*9.81 m/s^2= .938 m/s, but I don't know if that's a relevant equation.

Then I have an equation for angular velocity=Vt=wr

 

[LawrenceC]

Does a turntable turn clockwise? Normal force up, mg down, Ff opposite of the motion if clockwise then it's counterclock wise?

The turntable is turning at constant speed so you are not concerned with tangential force here. We want to determine what the maximum speed is.

At the point of impending coin movement outward, what forces are exactly balanced?

 

[LawrenceC]

"I have Vmax=SQRT Ws r g=SQRT .800*.12m*9.81 m/s^2= .938 m/s"

Use parentheses.

Your calculator seems to cause problems.

I am signing off for the day. You are on the right track.

Angular velocity = V/r

 

[SherBear]

The turntable is turning at constant speed so you are not concerned with tangential force here. We want to determine what the maximum speed is.

At the point of impending coin movement outward, what forces are exactly balanced?

I think the normal force and gravitational forced are the balanced forces.

 

[SherBear]

ok i did the calc with para, and the result was Vmax=.9704 m/s
then i plugged that into the m=v/r
.9704 m/s / .12 m = 8.09 rad/s ?

 

[LawrenceC]

That is what I calculated. Good work.

 

[SherBear]

Thank you Lawrence! and for all your help and hardwork also! :)