An airplane propeller is rotating at 2000 rev/min. A. Compute the propeller's angular velocity in rad/s .

B. How long in seconds does it take for the propeller to turn through 36∘?

A) The angular velocity of the propeller is 209.44 rad/s

B) The time it takes for the propeller to turn through 36° = 0.003 sec

Given data :

Airplane rotates at 2000 rev/min

A) Calculating the angular velocity of the propeller in rad/s

Given that : 180° = π rad ,  1 minute = 60 secs

Angular velocity = Δ angular rotation / Δ in time

∴ Angular velocity = (2000 ) * ( 2π ) * (1 / 60 )

                               = 209.44 rad/s

B) Determine how long it will take for the propeller to turn 36°

First step : convert angular velocity from A to degree/secs

               = 209.44 rad/s * ( 180 / π )  = 12,000 °/s

next step : determine the time taken ( t ) to turn through 36° using this relation below

36° = ( 12,000 degrees/sec ) * t

make t subject of the relation

∴ t = 36 / 12,000 = 0.003 sec.

Hence we can conclude that The angular velocity of the propeller is 209.44 rad/s and The time it takes for the propeller to turn through 36° = 0.003 sec.

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A 1 complete revolution corresponds to an angular displacement of 2π rad, or 360º. (So there are 180º for every π rad.) Also, there are 60 seconds to 1 minute. So, the angular velocity in rad/s is

(2000 rev/min) * (2π rad/rev) * (1/60 min/s) = 200π/3 rad/s

or approximately 209.44 rad/s.

B First convert the angular velocity to degrees per second (º/s):

(200π/3 rad/s) * (180/π º/rad) = 12,000 º/s

We want to find the time t it would take for the propeller to turn 36º:

36º = (12,000 º/s) t

==>  t = 36º / (12,000 º/s) = 3/1000 s

or approximately 0.003 s.

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