A-uniform-circular-disc-of-mass-1-5-kg-and-radius-0-5-m-is-initially-at-rest-on-a-horizontal-frictionless-surface-Three-forces-of-equal-magnitude-F-0-5-N-are-applied-simultaneously-along-the-three-

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Question Number 24934 by Tinkutara last updated on 29/Nov/17

$$\mathrm{A}\mathrm{uniform}\mathrm{circular}\mathrm{disc}\mathrm{of}\mathrm{mass}1.5\mathrm{kg}$$$$\mathrm{and}\mathrm{radius}0.5\mathrm{m}\mathrm{is}\mathrm{initially}\mathrm{at}\mathrm{rest}\mathrm{on}\mathrm{a}$$$$\mathrm{horizontal}\mathrm{frictionless}\mathrm{surface}.\mathrm{Three}$$$$\mathrm{forces}\mathrm{of}\mathrm{equal}\mathrm{magnitude}F=0.5\mathrm{N}$$$$\mathrm{are}\mathrm{applied}\mathrm{simultaneously}\mathrm{along}\mathrm{the}$$$$\mathrm{three}\mathrm{sides}\mathrm{of}\mathrm{an}\mathrm{equilateral}\mathrm{triangle}$$$$xyz\mathrm{with}\mathrm{its}\mathrm{vertices}\mathrm{on}\mathrm{the}\mathrm{perimeter}$$$$\mathrm{of}\mathrm{the}\mathrm{disc}.\mathrm{One}\mathrm{second}\mathrm{after}\mathrm{applying}$$$$\mathrm{the}\mathrm{forces},\mathrm{the}\mathrm{angular}\mathrm{speed}\mathrm{of}\mathrm{the}\mathrm{disc}$$$$\mathrm{in}\mathrm{rad}/\mathrm{s}\mathrm{is}:$$

Commented by Tinkutara last updated on 29/Nov/17

Commented by ajfour last updated on 29/Nov/17

$${\tau }_{net}=3\left(r_{\mathrm{\perp }}F\right)=3\times \frac{R}{2}\times F$$$$=\frac{3\times 0.5\times 0.5}{2}=\frac{3}{8}Nm$$$$\omega =\alpha △t=\left(\frac{{\tau }_{net}}{{MR}^2/2}\right)△t$$$$=\frac{3}{8}\times \frac{2}{1.5\times 0.5\times 0.5}\times 1$$$$=2rad/s.$$

Commented by Tinkutara last updated on 30/Nov/17

$$\mathrm{Thank}\mathrm{you}\mathrm{Sir}!$$

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