Rotational Velocity & Acceleration Video Lessons

Concept

# Problem: A 3.50 g coin is placed 11.0 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of μs = 0.890 and μk = 0.580.What is the maximum angular velocity with which the turntable can spin without the coin sliding?

###### FREE Expert Solution

Maximum static friction:

$\overline{){{\mathbit{f}}}_{{\mathbf{s}}}{\mathbf{=}}{{\mathbit{\mu }}}_{{\mathbf{s}}}{\mathbit{N}}}$

Newton's second law:

$\overline{){\mathbf{\Sigma }}{\mathbf{F}}{\mathbf{=}}{\mathbf{m}}{\mathbf{a}}}$

Centripetal acceleration:

$\overline{){{\mathbf{a}}}_{{\mathbf{c}}}{\mathbf{=}}\frac{{\mathbf{v}}^{\mathbf{2}}}{\mathbf{r}}{\mathbf{=}}{{\mathbf{r\omega }}}^{{\mathbf{2}}}}$

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###### Problem Details

A 3.50 g coin is placed 11.0 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of μs = 0.890 and μk = 0.580.

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