Converting rotational speed to angular velocity If a body rotates at N revolutions per minute (rpm), what is its angular velocity ω in radians per second?

Introduction / Context:Angular velocity is commonly required in radians per second for dynamics, power, and torque calculations. This question checks the fundamental conversion from rpm to rad/s.

Given Data / Assumptions:

• N is given in revolutions per minute (rpm).
• 1 revolution corresponds to 2π radians.
• 1 minute equals 60 seconds.

Concept / Approach:Use unit conversion: multiply by 2π radians per revolution and divide by 60 seconds per minute to convert rpm to rad/s.

Step-by-Step Solution:

Verification / Alternative check:For N = 60 rpm, ω should be 2π rad/s (one revolution per second). Substituting N = 60 gives ω = 2π, which matches.

Why Other Options Are Wrong:

• πN/60 or πN/180: Miss the factor of 2 for a full revolution (2π).
• 2πN/180: Divides by 180 instead of 60, underestimating by a factor of 3.
• N/2π: Inverts the correct relationship and has wrong units.

Common Pitfalls:Forgetting that 1 rev = 2π rad, or failing to convert minutes to seconds.

Final Answer:2πN/60