The angular velocity of a body is ω⃗=2 î+3 ĵ+4 k̂ and a torque τ⃗=î+2 ĵ+3 k̂ acts on it. The rot

step 1 Dear students, solution for problem 49 of chapter 7 is solution power p, power p is equal to tau

The angular velocity of a body is ω⃗=2 î+3 ĵ+4 k̂ and a...

The angular velocity of a body is $\vec{\omega}=2 \hat{i}+3 \hat{j}+4 \hat{k}$ and a torque $\vec{\tau}=\hat{i}+2 \hat{j}+3 \hat{k}$ acts on it. The rotational power will be
(a) $20 \mathrm{~W}$
(b) $15 W$
(c) $\sqrt{17} W$
(d) $\sqrt{14} W$

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Key Concepts

Rotational Power

Rotational power is the rate at which work is done in a rotating system. It is calculated by taking the dot product of the torque and angular velocity vectors, thereby indicating how effectively the applied torque contributes to the rotational motion of the system.

Dot Product (Scalar Product)

The dot product, or scalar product, is an operation that multiplies two vectors to produce a scalar. In physics, it is commonly used to calculate work or power, as it effectively projects one vector onto another by multiplying corresponding components and adding the results.

Angular Velocity

Angular velocity is a vector quantity that quantifies the rate of rotation and the axis about which a body rotates. It is typically expressed in radians per second and, as a vector, it indicates the direction of the rotation according to the right-hand rule.

Torque

Torque is a vector quantity representing the rotational equivalent of force. It measures the tendency of a force to produce rotation about an axis, with its magnitude determined by both the force applied and the lever arm, and its direction given by the right-hand rule.

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