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Rotational Mechanics Question

Q. A uniform metre stick of mass M is hinged at one end and supported in the horizontal direction by a string attached to the other end. What should be the initial angular acceleration of the stick if the string is cut?

a. $$\frac{3}{2}g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$$

b. $$g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$$

c. $$3g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$$

d. $$4g\hspace{2 mm}rad\hspace{1 mm}s^{-2}$$

The answer given was a... But i think it should be c. Pls solve this..

Note by Krishna Jha
4 years, 7 months ago

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The stick has moment of inertia $$I = \tfrac{1}{3}ML^2$$ about the hinge. The weight of the stick is $$W = Mg$$ and it acts at the center of mass which is $$d = \tfrac{1}{2}L$$ from the hinge. Initially, the weight is perpendicular to the stick. So, the total torque initially is $$\tau = Wd = \tfrac{1}{2}MgL$$. Since $$\tau = I\alpha$$, the initial angular acceleration is $$\alpha = \dfrac{\tau}{I} = \dfrac{\tfrac{1}{2}MgL}{\tfrac{1}{3}ML^2} = \dfrac{3g}{2L}$$. Plug in $$L = 1m$$ to get the answer.

- 4 years, 7 months ago

But L=1m is not given right??

- 2 years, 5 months ago

nice......just mingle around the formulas...as simple as that.

- 3 years, 10 months ago

Thanks...

- 4 years, 7 months ago