- #1
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This should be an easy one, but I can't fully figure it out.
If a ball is given some initial speed v0, but no angular speed as it's thrown on a surface with a coefficent of friction [itex]\mu[/itex], how long will it take for the ball to execute "perfect roll" ie. roll without slipping?
I did it through conservation of energy, and got
[tex]t = \frac{v_0}{\mu g}[/tex]
Next, I tried with Newton's laws.
I got
[tex]t = \frac{v_0}{\mu g\left(\frac{mr^2}{I} + 1\right)}[/tex]
I suppose the latter's wrong because I cannot simply assume the ball would only rotate about the center of mass -axis (that's what I did).
How do I take this into account?
If a ball is given some initial speed v0, but no angular speed as it's thrown on a surface with a coefficent of friction [itex]\mu[/itex], how long will it take for the ball to execute "perfect roll" ie. roll without slipping?
I did it through conservation of energy, and got
[tex]t = \frac{v_0}{\mu g}[/tex]
Next, I tried with Newton's laws.
I got
[tex]t = \frac{v_0}{\mu g\left(\frac{mr^2}{I} + 1\right)}[/tex]
I suppose the latter's wrong because I cannot simply assume the ball would only rotate about the center of mass -axis (that's what I did).
How do I take this into account?