Awheel increases its speed from 45 revolutions per minute to 90 revolutione per minute in 30 seconds.find angular acceralation of the wheel and number of revolution made by this wheel in this 30 seconds.
angular acc. =1.5
To find the angular acceleration of the wheel, we can use the formula:
Angular acceleration = (final angular velocity - initial angular velocity) / time
Given:
Initial angular velocity (ω1) = 45 revolutions per minute
Final angular velocity (ω2) = 90 revolutions per minute
Time (t) = 30 seconds
Step 1: Convert the initial and final angular velocities to revolutions per second.
Divide both ω1 and ω2 by 60 to convert from revolutions per minute to revolutions per second.
ω1 = 45 revolutions per minute / 60 = 0.75 revolutions per second
ω2 = 90 revolutions per minute / 60 = 1.5 revolutions per second
Step 2: Calculate the angular acceleration.
Angular acceleration = (ω2 - ω1) / t
Angular acceleration = (1.5 revolutions per second - 0.75 revolutions per second) / 30 seconds
Angular acceleration = 0.75 revolutions per second / 30 seconds
Angular acceleration = 0.025 revolutions per second²
Therefore, the angular acceleration of the wheel is 0.025 revolutions per second².
Next, let's find the number of revolutions made by the wheel in this 30 seconds.
Step 3: Calculate the average angular velocity.
Average angular velocity = (initial angular velocity + final angular velocity) / 2
Average angular velocity = (ω1 + ω2) / 2
Average angular velocity = (0.75 revolutions per second + 1.5 revolutions per second) / 2
Average angular velocity = 1.25 revolutions per second
Step 4: Calculate the angle covered in 30 seconds using the average angular velocity.
Angle covered = average angular velocity * time
Angle covered = 1.25 revolutions per second * 30 seconds
Angle covered = 37.5 revolutions
Therefore, the wheel made 37.5 revolutions in the given 30 seconds.