Question

An electric saw uses a circular spinning blade to slice through wood. When you start the saw, the motor needs 2.00 seconds of constant angular acceleration to bring the blade to its full angular velocity. If you change the blade so that the rotating portion of the saw now has 3.00 times its original rotational mass, how long will the motor need to bring the blade to its full angular velocity

Answer 1

Answer:

6 seconds

Explanation:

So suppose the new saw has the same mass distribution, only difference in mass density, then the moment of the new saw would be 3 times the original ones.

Suppose both saws are under the same torque, by Newton's 2nd law, we have the following equation of angular acceleration related to torque T and moment of inertia I:

$\alpha = \frac{T}{I}$

So if I is tripled while T stays the same, α would have been reduced 3 times

So to achieve the full angular velocity:

$\omega = \alpha t$

Now that angular acceleration is reduced 3 times. The time it takes would have to be 3 times as much, or 2 * 3 = 6 seconds.