The rectangle shown has a mass, m. The sides are made of uniform thin wire. The short side is of length a, and the long side is of length b. If m = 10.50 g, a = 35.00 cm and b = 71.4 cm, what is the moment of rotational inertia about the axis indicated?
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To find the moment of rotational inertia about the axis indicated, we need to use the formula for the moment of inertia of a rectangular plate rotated about an axis perpendicular to its plane and passing through one of its sides.
The formula for the moment of inertia of a rectangle about an axis through one of its sides is given by:
I = (1/3) * m * (a^2 + b^2)
Where:
I is the moment of inertia
m is the mass of the rectangle
a is the length of the shorter side of the rectangle
b is the length of the longer side of the rectangle
In this case, m = 10.50 g = 0.0105 kg, a = 35.00 cm = 0.35 m, and b = 71.4 cm = 0.714 m.
Plugging these values into the formula:
I = (1/3) * 0.0105 kg * (0.35^2 + 0.714^2)
I = (1/3) * 0.0105 kg * (0.1225 + 0.510996)
I = (1/3) * 0.0105 kg * 0.633496
I = 0.00211 kg.m^2
Therefore, the moment of rotational inertia about the given axis is 0.00211 kg.m^2.