The angular velocity (in rad/s) of a body rotating at N r.p.m. isa)π N/60b)2 π N/60c)π N/120d)π N/180Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Angular velocity is defined as the rate of change of angular displacement with respect to time. It is usually expressed by a Greek letter ω (omega).

Mathematically, angular velocity,

ω =dθ/dt

If a body is rotating at the rate of N r.p.m. (revolutions per minute), then its angular velocity,

ω = 2πΝ / 60 rad/s

Answer

Explanation:

In order to solve this question, we need to have a clear understanding of the terms 'angular velocity' and 'r.p.m.'

Angular velocity: It is defined as the rate of change of angular displacement with respect to time. Angular velocity is measured in radians per second (rad/s).

r.p.m.: It stands for revolutions per minute. It is a measure of the rotational speed of an object.

Formula:

The formula to calculate angular velocity of a rotating body is:

Angular velocity (ω) = Δθ/Δt

where Δθ is the change in angular displacement and Δt is the change in time.

Since 1 revolution = 2π radians, we can convert r.p.m. to radians per second using the following formula:

1 revolution = 2π radians

1 minute = 60 seconds

Therefore, angular velocity (in rad/s) = (2π/60) × N = πN/30

Solution:

Given, the body is rotating at N r.p.m.

Using the above formula, we get:

Angular velocity (in rad/s) = πN/30

Substituting N = 60 (since we need to convert r.p.m. to rad/s), we get:

Angular velocity (in rad/s) = (π × 60)/30 = 2π

Therefore, the correct answer is option B, i.e., 2πN/60.

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