A circular saw blade rotation at 3600 rpm is reduced to 3450 rpm in 2 sec. What is the angular acceleration of the blade?
To calculate the angular acceleration of the blade, we need to use the formula:
Angular acceleration (α) = (Final angular velocity (ωf) - Initial angular velocity (ωi)) / Time (t)
Given:
Initial angular velocity (ωi) = 3600 rpm
Final angular velocity (ωf) = 3450 rpm
Time (t) = 2 sec
First, we need to convert the angular velocities from rpm (revolutions per minute) to radians per second. Since 1 revolution is equal to 2π radians, we can convert rpm to rad/s using the following conversion factor:
1 rpm = (2π radians) / 60 seconds
So, we have:
Initial angular velocity (ωi) = (3600 rpm) * ((2π radians) / 60 seconds)
Final angular velocity (ωf) = (3450 rpm) * ((2π radians) / 60 seconds)
Plugging in the values:
Initial angular velocity (ωi) = (3600 rpm) * ((2π radians) / 60 seconds) ≈ 376.99 rad/s
Final angular velocity (ωf) = (3450 rpm) * ((2π radians) / 60 seconds) ≈ 360.87 rad/s
Now we can calculate the angular acceleration:
Angular acceleration (α) = (360.87 rad/s - 376.99 rad/s) / 2 seconds
≈ -8.06 rad/s^2
Therefore, the angular acceleration of the blade is approximately -8.06 rad/s^2. The negative sign indicates a deceleration or a decrease in angular velocity.