A variable-speed drill, initially turning at 150 rpm, speeds up to 1300 rpm in a time interval of 1.0 s. What is its average rotational acceleration?


----rpm/s2

See previous post: Sat, 10-29-16, 9:35 AM.

To find the average rotational acceleration, we need to use the formula:

Average rotational acceleration = (final rotational speed - initial rotational speed) / time

Given:
Initial rotational speed (ω₁) = 150 rpm
Final rotational speed (ω₂) = 1300 rpm
Time interval (t) = 1.0 s

First, let's convert the rotational speed from rpm to rad/s:
1 revolution = 2π radians
1 minute = 60 seconds

Initial rotational speed (ω₁) = 150 rpm = (150 * 2π) / 60 rad/s = 5π rad/s
Final rotational speed (ω₂) = 1300 rpm = (1300 * 2π) / 60 rad/s = 65π rad/s

Now, substitute the values into the formula:

Average rotational acceleration = (65π - 5π) / 1.0
= 60π rad/s / 1.0 s
= 60π rad/s²

Therefore, the average rotational acceleration is 60π rad/s², or approximately 188.5 rad/s².