How can angular velocity of a rotating system be calculated?

The calculation of angular velocity in a rotating system is accurately represented by taking the angle of rotation and dividing it by the time taken for that rotation. Angular velocity is typically measured in radians per second and reflects how quickly an object rotates around a central point or axis. It quantifies the angle traversed over a specific duration.

This approach directly ties the concept of angular motion to time, providing a clear and direct relationship that is fundamental in physics. When a rotating object completes one full revolution, it has rotated through an angle of (2\pi) radians; therefore, if you know how long it took to complete this rotation, you can easily compute the angular velocity by dividing the total angle by the time taken.

The other choices do not correctly define how to calculate angular velocity. For instance, multiplying linear speed by the radius gives the tangential acceleration or can relate to the linear and angular velocities, but it does not provide the angular velocity directly. Measuring the frequency of rotation in hertz corresponds to how many cycles occur per second but does not provide the angular displacement per unit time without further conversion. Adding linear speed to angular speed lacks relevance as they pertain to different kinds of motion — linear and rotational — and cannot be simply summed up. Therefore