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

V = Vo + a*t.

1300 = 150 + a*1, a = 1150 rpm/s^2.

To find the average rotational acceleration, we need to determine the change in rotational speed and the time interval over which this change occurs.

The change in rotational speed is given by:

Δω = ωf - ωi

Where:
Δω = change in rotational speed
ωf = final rotational speed = 1300 rpm
ωi = initial rotational speed = 150 rpm

Substituting the values, we have:

Δω = 1300 rpm - 150 rpm
Δω = 1150 rpm

Now, divide the change in rotational speed by the time interval to find the average rotational acceleration:

Average acceleration = Δω / Δt

Where:
Δt = time interval = 1.0 s

Substituting the values, we have:

Average acceleration = 1150 rpm / 1.0 s
Average acceleration = 1150 rpm/s

Therefore, the average rotational acceleration of the variable-speed drill is 1150 rpm/s.

To find the average rotational acceleration, we can use the equation for rotational acceleration:

Rotational acceleration (α) = (final angular velocity - initial angular velocity) / time interval

First, we need to convert the initial and final angular velocities from RPM to rad/s. Recall that 1 revolution is equal to 2π radians.

So, the initial angular velocity (ω-initial) is:
ω-initial = 150 rpm * (2π rad/1 min) * (1 min/60 s)
ω-initial = 150 * (2π / 60) rad/s

Similarly, the final angular velocity (ω-final) is:
ω-final = 1300 rpm * (2π rad/1 min) * (1 min / 60 s)
ω-final = 1300 * (2π / 60) rad/s

Now we can substitute these values into the formula for rotational acceleration:

α = (ω-final - ω-initial) / time interval

α = (ω-final - ω-initial) / 1.0 s

α = (1300 * (2π / 60) - 150 * (2π / 60)) / 1.0 s

α = (1300 - 150) * (2π / 60) / 1.0 s

α = 1150 * (2π / 60) / 1.0 s

Now we can calculate the value of α:

α ≈ 120.74 rad/s²

So, the average rotational acceleration of the variable-speed drill is approximately 120.74 rad/s².