Answer to Question #123782 in Mechanics | Relativity for Ojugbele Daniel

Question #123782
The angular velocity of a disc of mass 3kg and radius 0.6m change from 10rev/s to 15rev/s in 0.07s. calculate the impulse on the disc.
1
Expert's answer
2020-06-29T14:14:04-0400

Angular momentum L (which change disc speed) can be found:

L=J(ω2ω1)L=J*(\omega_{2} - \omega_{1})

where J - disc's moment of inertia, ω2 - finish angular speed ω1 - start angular speed.

Moment of inertia for disc can be found:

J=m×r22J= \frac{m\times r^2}{2}

where m - mass of the disc, r - radius of the disc.

Angular speed for correct calculation have to be transformed from rev/s to rad/s.

1rev/s=2×πrad/s1 rev/s = 2\times\pi rad/s


So we have:

L=m×r2×(ω2ω1)2L=\frac{m\times r^2\times(\omega_{2}-\omega_{1})}{2}

L=3×0.62×(15×2×π10×2×π)2=16.956kg×m2sL=\frac{3\times0.62\times(15\times2\times\pi - 10\times2\times\pi)}{2}=16.956 \frac{kg\times m^2}{s}


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