The propeller of a plane rotate clockwise at 31800 rpm. What is the angular acceleration (in rad/s2) of the propeller if it takes 6.00 s to come to a standstill? Give your answer as a positive value.
Question
The propeller of a plane rotate clockwise at 31800 rpm. What is the angular acceleration (in rad/s2) of the propeller if it takes 6.00 s to come to a standstill? Give your answer as a positive value.
Solution
First, we need to convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s).
1 revolution is equal to 2π radians, and 1 minute is equal to 60 seconds.
So, the initial angular speed (ωi) is:
ωi = 31800 rpm * (2π rad / 1 rev) * (1 min / 60 s) = 3330.6 rad/s
The final angular speed (ωf) is 0 rad/s, because the propeller comes to a standstill.
The time (t) it takes for the propeller to come to a standstill is given as 6.00 s.
Angular acceleration (α) can be calculated using the formula:
α = (ωf - ωi) / t
Substituting the given values into the formula, we get:
α = (0 rad/s - 3330.6 rad/s) / 6.00 s = -555.1 rad/s²
However, the question asks for the answer as a positive value, so we take the absolute value:
α = 555.1 rad/s²
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