Angular Velocity Calculation for Spinning Barbell

What is the angular velocity of the spinning barbell?

Given the mass (m) of each ball, the distance (d) between the centers of the balls, the speed (vcm) of the center of mass, and the time taken to make one complete revolution, what is the angular velocity of the spinning barbell?

Answer:

The angular velocity of the spinning barbell can be calculated using the formula ω = 2π / t, where t is the time for one complete revolution. Without the value of t, we cannot determine the correct answer from the multiple-choice options.

To find the angular velocity of the spinning barbell, we need to understand the relationship between angular displacement, time, and angular velocity. One complete revolution means that the angular displacement is 2π radians. If t represents the time taken for one complete revolution, we can find the angular velocity (denoted as ω) using the following equation:

ω = Δθ / Δt = 2π / t

Without the value for the time (t), we cannot calculate an exact numerical value for the angular velocity (ω). However, if the time for one complete revolution is known, the student should simply substitute that value into the numerator of the equation above to get the angular velocity in radians per second (rad/s).

For example, if the time for one revolution is 2 seconds, then using the formula above:

ω = 2π / 2 = π rad/s = approximately 3.14 rad/s.

This would correspond to an answer not listed in the multiple-choice options provided.