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Torque is a central concept in rotational dynamics. It measures how effectively a force can rotate an object about an axis. Think of it as the rotational equivalent of linear force. To understand torque, imagine opening a door. The force applied at the door's handle creates torque about the hinges. The farther the handle is from the hinge, the greater the torque for the same applied force. This relationship is mathematically expressed as:\[ \text{Torque} (\tau) = \text{Force} \times \text{Lever Arm} \]In the exercise provided, torque is given directly as a value \(\left(\frac{5}{\pi}\right) \times 10^{-6} \text{ Nm}\). This means there is a force acting on a specific point on a rotating body, causing it to spin.Understanding the concept of torque will help you conceptualize problems involving rotational motion and understand how forces affect rotational systems.

Angular velocity describes how quickly an object rotates around a point or axis. It is akin to linear velocity but in a rotational context. The standard unit for angular velocity is radians per second \(\text{rad/s}\). To convert revolutions per second into radians per second, recall that one full circle is \(2\pi\) radians.For example, if a body completes 2 revolutions in one second, its angular velocity would be:\[ \text{Angular Velocity} (\omega) = 2 \times 2\pi = 4\pi \text{ rad/s} \]This calculation is vital for understanding how fast something is rotating. In our problem, knowing the angular velocity allows us to calculate the rotational power applied to the body as it spins.

Revolutions per second is a measure of rotational speed. It tells us how many complete turns a rotating object makes each second. This measurement is often used in contexts like motors, gears, and turbines to express how fast these systems operate. By itself, revolutions per second is intuitive - more revolutions mean faster rotation.In scientific and engineering contexts, it’s crucial to translate revolutions into radians to work with other rotational formulas. As noted earlier, 1 revolution equals \(2\pi\) radians. Therefore:- 2 revolutions per second equals \(4\pi\) radians per second.Converting revolutions to radians is necessary for further calculations, such as finding angular velocity and, subsequently, computing rotational power in our problem.