First slide

Circular motion in horizontal plane

Question

A coin is placed at the edge of a horizontal disc rotating about a vertical axis through its axis with a uniform angular speed 2 rad $s^{- 1}$ . The radius of the disc is 50 cm. Find the minimum coefficient of friction between disc and coin so that the coin does not slip (g = 10 m $s^{- 2}$ ).

Moderate

A

0.1
B

0.2
C

0.3
D

0.4

Solution

$f_{1} = μ m g$ ,friction will provide the necessary centripetal force $f = m w^{2} r$
$f \leq f_{l} \Rightarrow m w^{2} r \leq μ m g$
$μ \geq \frac{ω^{2} r}{g} = \frac{2^{2} \times 50 / 100}{10}$
$μ \geq 0.2$

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