The angular velocity of an engine increase from 1200 RPM to 3000 RPM in 10 second computer angular acceleration and the number of revolution made during this time.
Change in angular velocity is 3000 rpm - 1200 rpm = 1800 rpm.
This happens over a period of 10 seconds, or 1/6 of a minute.
Angular acceleration
= change in angular velocity/change in time
= 1800/(1/6)
= 10800 rpm^2
Number of rotations made during this time
= 1800 rotations per minute x 1/6 minute
= 300 rotations
To compute the angular acceleration, we can use the formula:
angular acceleration (α) = (final angular velocity - initial angular velocity) / time taken
Given:
Initial angular velocity (ω1) = 1200 RPM
Final angular velocity (ω2) = 3000 RPM
Time taken (t) = 10 seconds
Substituting these values into the formula, we can find the angular acceleration:
α = (3000 - 1200) / 10
α = 180 radians per second squared
To find the number of revolutions made during this time, we can use the formula:
number of revolutions = (final angular velocity - initial angular velocity) / (2π)
Substituting the values into the formula, we can calculate the number of revolutions:
number of revolutions = (3000 - 1200) / (2π)
number of revolutions = 180 / π
number of revolutions ≈ 57.30
To compute the angular acceleration, we can use the formula:
Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time taken
In this case, the initial angular velocity (ω₁) is 1200 RPM, the final angular velocity (ω₂) is 3000 RPM, and the time taken (t) is 10 seconds.
Let's first convert the angular velocities from RPM (revolutions per minute) to radians per second (rad/s), as angular acceleration is usually measured in radians per second squared (rad/s²).
1 revolution = 2π radians
1 minute = 60 seconds
Initial angular velocity in rad/s:
ω₁ = 1200 RPM
= 1200 * (2π radians) / (1 minute)
= 1200 * (2π radians) / (60 seconds)
= 40π rad/s
Final angular velocity in rad/s:
ω₂ = 3000 RPM
= 3000 * (2π radians) / (1 minute)
= 3000 * (2π radians) / (60 seconds)
= 100π rad/s
Now, let's substitute these values into the formula:
α = (ω₂ - ω₁) / t
= (100π - 40π) / 10
= 6π rad/s²
So the angular acceleration of the engine is 6π rad/s².
To compute the number of revolutions made during this time, we can use the formula:
Number of revolutions = (Final angular velocity - Initial angular velocity) / (2π)
Again, substituting the values:
Number of revolutions = (100π - 40π) / (2π)
= 60 revolutions
Therefore, the engine has made 60 revolutions during this time.