Question

An electric saw uses a circular spinning blade to slice through wood. When you start the saw, the motor needs 2 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 three times its original rotational mass, how long will the motor need to bring the blade to its full angular velocity

Answer 1

6 s

Step-by-step explanation:

Let angular acceleration=
`\alpha`

Rotational mass=I

Time,t=2 s

`I'=3 I`

Angular acceleration,
`\alpha=(\tau)/(I)`...(1)

`\alpha'=(\tau)/(3I)`...(2)

Equation(2) divided by equation (1)

`(\alpha')/(\alpha)=(1)/(3)`

`\alpha'=(1)/(3)\alpha`

`\alpha=(\omega-\omega_0)/(t)`

When alpha decreases by 1/3 factor then time increases by 3

The motor needs 2 s originally.If the rotational mass is 3 times the original rotational mass then it takes 3 times the original time.

Time=
`2* 3=6 s`

Hence, the motor need to bring the blade to its full angular velocity=6 s