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A uniform of mass m and length L is tied...

A uniform of mass `m` and length `L` is tied to a vertical shaft. It rotates in horizontal plane about the vertical axis at angular velocity `omega`. How much horizontal force does the shaft exert on the rod?

Text Solution

Verified by Experts

Let `T` be the force applied horizontally on the rod. The acceleration of the centre of mass is `omega^(2)(L/2)` as it moving in a circle of radius `L/2`.

Using `vecF_(ext)=Mveca_(cm)impliesT=Momega^(2)(L/2)`
Thus, the horizontal force exerted is `1/2Momega^(2)L`.
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Knowledge Check

  • A rod AB of mass m and length l is rotating about a vertical axis as shown. It's moment of inertia about this axis is :

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