A uniform disc of radius R = 0.2 m is projected along a rough horizontal surface with initial linear velocity v 0 = 2 m/s and initial angular velocity ω 0 = 5 rad/s as shown in the figure. Coeffic

Question

A uniform disc of radius R = 0.2 m is projected along a rough horizontal surface with initial linear velocity v 0 ​ = 2 m/s and initial angular velocity ω 0 ​ = 5 rad/s as shown in the figure. Coefficient of friction is μ = 0.1 . The time (in second) at which it starts pure rolling is. (Take g = 10 m/s 2 )

TestHub · Accepted Answer

Take clockwise angular velocity as positive. Initially the spin is counter-clockwise.

$v_{0} = 2, ω_{0} = - 5$

$F_{f} = μ m g, v = 2 - t$

$α = \frac{F _{f} R}{m R ^{2} /2} = 10 rad/ s^{2}$

$ω = - 5 + 10 t$

$v = ω R \Rightarrow 2 - t = 0.2 (- 5 + 10 t)$

$t = 1 s$

Answer 1.

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