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.
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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