A rectangular steel plate of mass has length and width

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A rectangular steel plate of mass

4.0\,\text{kg}

has length

0.50\,\text{m}

and width

0.30\,\text{m}

. Consider two parallel axes that are perpendicular to the plane of the plate: • Axis A passes through the plate’s center. • Axis B is parallel to Axis A and passes through a point

0.20\,\text{m}

away from the center along the length of the plate. (For a rectangle of sides

L

and

W

about a central axis perpendicular to its plane,

I_{\text{cm}}=\tfrac{1}{12}M\left(L^{2}+W^{2}\right)

.) (a) Calculate the rotational inertia of the plate about Axis A. (b) Calculate the rotational inertia of the plate about Axis B. (c) A machine part specification limits the allowable rotational inertia to

0.12\,\text{kg}\cdot\text{m}^2

. Identify which, if any, of the two axes meets this specification and justify your choice quantitatively.

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