First slide

Rolling motion

Question

A homogeneous solid ball is placed on an inclined plane making an angle $θ$ with the horizontal. At what values of the coefficient of friction $μ$ will the ball roll down the plane without slipping?

Moderate

A

$\geq \frac{2}{7} tanθ$
B

$\geq \frac{2}{5} tanθ$
C

$\geq \frac{2}{3} tanθ$
D

$\geq \frac{3}{4} tanθ$

Solution

$μ \geq \frac{tanθ}{1 + \frac{{MR}^{2}}{I}} \Rightarrow μ \geq \frac{tanθ}{1 + \frac{{MR}^{2}}{(\frac{2}{5}) {MR}^{2}}} = \frac{2}{7} \tan θ$

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