Coin kept at distance 10 cm from center of the table

Question

A coin is kept at a distance 10 cm from the centre of turn table of radius 1 m just begins to slip, when the turn table rotates at speed of 90 r. p. m. Calculate the coefficient of static friction between coin and the turntable. ( g = 9.8 m/s²).

Answer 1

Given,

r = 10 cm = 0.1 m

radius at which it steps,

Centrifugal force = Remaining static friction

⇒ μ_smg = mrω²

ω = 90rpm

= \(\frac{90\times 2\pi}{60}\) rad/s

= 1.5 x 2π

= 3π rad/s

⇒ μ_s x m x 9.8  = m x 0.1 x 9π²

⇒ μ_s =  \(\frac{0.1\times 9 \times 9.8}{9.8}\)

= 0.9