(A) The rotational power $(P)$ is given by the dot product of torque $(\vec{\tau})$ and angular velocity $(\vec{\omega})$.$P = \vec{\tau} \cdot \vec{\

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(A) The rotational power $(P)$ is given by the dot product of torque $(\vec{\tau})$ and angular velocity $(\vec{\omega})$.$P = \vec{\tau} \cdot \vec{\omega}$Given $\vec{\tau} = \hat{i} + 2\hat{j} + 3\hat{k}$ and $\vec{\omega} = 2\hat{i} + 3\hat{j} + 4\hat{k}$.$P = (1\hat{i} + 2\hat{j} + 3\hat{k}) \cdot (2\hat{i} + 3\hat{j} + 4\hat{k})$$P = (1 \times 2) + (2 \times 3) + (3 \times 4)$$P = 2 + 6 + 12$$P = 20 \ W$

Class 11 Physics System of Particles and Rotational Motion Energy conservation, Kinetic Energy, Work and Power of Rotational Motion

Easy

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 .......... $W$.

A
$20$
B
$15$
C
$\sqrt{17}$
D
$\sqrt{14}$

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Class 11 Questions

Class 11

Physics Questions

Chapter

System of Particles and Rotational Motion

Subtopic

Energy conservation, Kinetic Energy, Work and Power of Rotational Motion

$A$ constant power is supplied to a rotating disc. The angular velocity $(\omega)$ of the disc varies with the number of rotations $(n)$ made by the disc as:

Medium

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$A$ tangential force $F$ is applied on the rim of a ring of radius $R$. If the ring rotates by an angle $\theta$,what is the work done by the force?

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$A$ rod of length $1 \ m$ is held vertically and allowed to fall such that its lower end remains fixed on the ground. The velocity of the other end of the rod when it hits the ground is ......... $m/s$ $(g = 9.8 \ m/s^2)$.

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$A$ wheel of moment of inertia $10 \ kg \cdot m^2$ is rotating at $10$ rotations per minute. The work done in increasing its speed to $5$ times its initial value will be .......... $J$.

Medium

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Write the formula for power in the motion of a rigid body.

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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 .......... $W$.

Similar Questions

$A$ constant power is supplied to a rotating disc. The angular velocity $(\omega)$ of the disc varies with the number of rotations $(n)$ made by the disc as:

$A$ tangential force $F$ is applied on the rim of a ring of radius $R$. If the ring rotates by an angle $\theta$,what is the work done by the force?

$A$ rod of length $1 \ m$ is held vertically and allowed to fall such that its lower end remains fixed on the ground. The velocity of the other end of the rod when it hits the ground is ......... $m/s$ $(g = 9.8 \ m/s^2)$.

$A$ wheel of moment of inertia $10 \ kg \cdot m^2$ is rotating at $10$ rotations per minute. The work done in increasing its speed to $5$ times its initial value will be .......... $J$.

Write the formula for power in the motion of a rigid body.

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