A variable-speed drill, initially turning at 250 rpm, speeds up to 1300 rpm in a time interval of 0.1 s. What is its average rotational acceleration?
{[(1300 - 250) / 60] * 2 π / 0.1} rad/s^2
To determine the average rotational acceleration of the drill, we can use the formula:
Average rotational acceleration = (final angular velocity - initial angular velocity) / time interval
In this case, the initial angular velocity of the drill is 250 rpm, which can be converted to radians per second by multiplying by 2π/60:
Initial angular velocity = 250 rpm * (2π/60) rad/s ≈ 26.1799 rad/s
The final angular velocity is 1300 rpm, which can also be converted to radians per second using the same conversion factor:
Final angular velocity = 1300 rpm * (2π/60) rad/s ≈ 136.6592 rad/s
The time interval is given as 0.1 s.
Now, we can calculate the average rotational acceleration:
Average rotational acceleration = (136.6592 rad/s - 26.1799 rad/s) / 0.1 s ≈ 1104.792 rad/s²
Therefore, the average rotational acceleration of the drill is approximately 1104.792 rad/s².