Question

"Which equation should one use to solve the following problem: A flywheel with mass 120 kg, and radius 0.6 m, starting at rest, has an angular acceleration of 0.1 rad/s2. How many revolutions has the wheel undergone after 10 s

Answer 1

You can use the equation . . .

D = (1/2) (a) (T²)

D is distance

a is acceleration

T is time

I realize this is actually the equation for linear motion, and they use different letters when it's talking about rotary motion. But the two equations are exactly the same thing, but I can't remember the letters used for the rotary case, and this is the way I like to remember it.

It reminds me that it's exactly the same thing happening in both cases, and I don't see any good reason to clutter up my mind with two copies of the same equation using different letters.

In this particular question, notice that you don't need to use or even know the mass OR the radius of the flywheel. Those numbers are just there to see if you know what you're doing, and you never use them. If there were more parts to the question, you might need them. But not as far as this question goes here.

Answer 2

To solve this problem it is necessary to apply the concepts related to the kinematic equations of angular motion description.

To find the angular displacement you have to

`\theta = \omega_0t+(1)/(2)\alpha t^2`

Where,

`\theta =` Angular displacement

`\omega_0 =` Angular velocity

`\alpha =` Angular acceleration

t = time

From our dates we have that

`m=120kg`

`R=0.6m`

`\omega=0rad/s`

`\alpha=0.1rad/s^2`

`t= 10s`

Replacing,

`\theta = \omega_0t+(1)/(2)\alpha t^2`

`\theta = (0)(10)+(1)/(2) (0.1)(10)^2`

`\theta =5rad`

In revolutions the value can be calculated as,

`\#Revolution = (\theta)/(2\pi)`

`\#Revolution = (5)/(2\pi)`

`\#Revolution = 0.8Revolution`

Therefore the number of revolutions is 0.8