A music compact disc does ninety revolutions in one minute. Calculate its angular velocity in rad/s
90 rev/min * 2πrad/1rev * 1min/60s = 3π rad/s
A musical compact 45
To calculate the angular velocity of a compact disc, we need to use the formula:
Angular velocity (ω) = 2π × Number of revolutions ÷ Time
First, let's convert the number of revolutions per minute to revolutions per second since time is typically measured in seconds.
Given:
Number of revolutions = 90 per minute
Time = 1 minute
Number of revolutions per second = Number of revolutions ÷ 60 seconds
So, the angular velocity can be calculated as:
Angular velocity (ω) = 2π × (90 ÷ 60)
Simplifying,
Angular velocity (ω) = 2π × 1.5
Finally, calculating the value:
Angular velocity (ω) ≈ 9.42 rad/s
Therefore, the angular velocity of the music compact disc is approximately 9.42 rad/s.