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
change in rad/s = 1150 revs/min /1s
= 1150 rev/min * 1 min/60 s * 2pi rad/rev /1 s
To find the average rotational acceleration, we first need to calculate the change in rotational speed and the time interval. Then we can use the formula for average acceleration.
The change in rotational speed (Δω) can be calculated by subtracting the initial speed from the final speed:
Δω = Final speed - Initial speed
Δω = 1300 rpm - 150 rpm
Δω = 1150 rpm
Now we have the change in rotational speed. The time interval is given as 1.0 s.
To find the average rotational acceleration (α), we can use the following formula:
α = Δω / Δt
where α is the average rotational acceleration, Δω is the change in rotational speed, and Δt is the time interval.
Let's substitute the values into the formula:
α = 1150 rpm / 1.0 s
Since we want the units to be in rpm/s^2, we need to convert the rotational speed to rpm/s:
1 rpm = 1/60 rev/s
We can now convert the units:
α = (1150 rpm / 1.0 s) * (1 rev / 60 rpm) * (1/60 s)
α ≈ 0.319 rpm/s^2
Therefore, the average rotational acceleration of the drill is approximately 0.319 rpm/s^2.