Final answer:
To find the angular velocity of a turntable rotating at 45 rev/min, we convert revolutions to radians and minutes to seconds, resulting in an angular velocity of 4.712 rad/s. However, this is not one of the provided options. The closest option to the calculated value is 90π rad/min.
Step-by-step explanation:
To calculate the angular velocity of the turntable, we need to convert revolutions per minute into radians per second. Since there are 2π radians in one revolution, and there are 60 seconds in a minute, the calculation for the turntable rotating at 45 rev/min is as follows:
ω = 45 rev/min × (2π radians/rev) ÷ (1 min/60 s)
Doing the math:
ω = (45 × 2π) ÷ 60 rad/s
ω = 90π ÷ 60 rad/s
ω = 1.5π rad/s
Converting 1.5π radians to decimals gives us ω = 4.712 rad/s. However, this option is not provided in the multiple choice answers. By looking at the possible choices and based on the calculation, the closest option and the correct answer is:
B. 90π rad/min