The angular velocity of a body is - - 2i - 3j - 4k and a torque - - i - 2j - 3k acts on it- The rotational power will be

Power (P) = τ⃗.ω⃗ = (i+2j+3k).(2i+3j+4k) = 2+6+12 = 20 W ...

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Rotational Power

The angular v...

Question

The angular velocity of a body is $\to ω = 2 ˆ i + 3 ˆ j + 4 ˆ k$ and a torque $\to τ = ˆ i + 2 ˆ j + 3 ˆ k$ acts on it. The rotational power will be

20 W

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15 W

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\sqrt{17} W

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\sqrt{14} W

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Solution

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\to ω = 2 ˆ i + 3 ˆ j + 4 ˆ k

\to τ = ˆ i + 2 ˆ j + 3 ˆ k

\to ω = 3^i + 2^j + 3^k

\to τ = 2^i + + 3^j + 4^k

\to i + \to 2 j + \to 3 k

\to i - \to 2 j + \to 5 k

\to 3 j - \to 4 k

- \to 2 i + \to 3 j - \to 3 k

2 ¯ i - 3 ¯ j + 4 ¯ ¯ ¯ k, ¯ i - 2 ¯ j + 3 ¯ ¯ ¯ k

3 ¯ i + ¯ j - 2 ¯ ¯ ¯ k

F = (2 ˆ i - 3 ˆ j + 4 k)

r = (3 ˆ i + 2 ˆ j + 3 ˆ k)

τ = r \times F

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