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Question: A uniform square plate of mass 0.5 kg and edge 20 cm is rotating about one of its diagonals at the r...

A uniform square plate of mass 0.5 kg and edge 20 cm is rotating about one of its diagonals at the rate of 180 revolutions per minute. The angular momentum of the square plate about its axis of rotation is

A

2π×10−2 kg-m2/s

B

π× 10−2 kg-m2/s

C

3π× 10−2 kg-m2/s

D

5π× 10−2 kg-m2/s

Answer

π× 10−2 kg-m2/s

Explanation

Solution

Moment of inertia of square plate about one of its diagonals is

I = ma212=0.5×0.2212\frac{ma^{2}}{12} = \frac{0.5 \times 0.2^{2}}{12} = 0.5×4×10−212\frac{0.5 \times 4 \times 10^{- 2}}{12}

= 53\frac{5}{3}×10−3 kg-m2

Angular velocity ω = 2πN/60 = 2π×180/60=6π rad/s

∴ Angular momentum L= Iω = 53\frac{5}{3}×10−3 × 6π

= π × 10−2 kg-m/s2

Hence, (2) is the correct