Inertia (Physics)?

Question

A centrifuge rotor has a moment of inertia of 3.25 10-2 kgm2. How much energy is required to bring it from rest to 10000 rpm?
J

the moment of inertia i is 3.25*10^(-2) kg.m^2

Answer 1

It is very interesting indeed.
One may look at a moment of inertia as a rotational mass.
For a solid rotor or a cylinder it is I=0.5(mr^2) (see ref 1)

But what we really need is;
The rotational energy Er =0.5(Iw^2) (or kinetic energy of rotation.)
W- rotational speed
w=2 Pi (f)=2Pi(RPM * 60)
I moment of inertia

Er = Energy in question and we have (ref 2)

Er=.5*(3.25 10-2)*(2 *(3.14) *1000 * 60) =
E=6126 Joules

Answer 2

Inertia of body is a property by virtue of which the body opposes to change in its state of motion or rest. So, according to this if you push a book which is on a table you can feel that it will start moving only after the push has reached to a certain limit. Same experiments can be done with pencil or any other object.

Answer 3

First convert RPM into revolution per second.
In one minute (60 seconds) the number of revolutions is 10000.
In one second the number of revolution is (10000/60).
One revolution means 2pi radian.
(10000/60) revolution means, 2 x pi x (1/60) 10000 =1047radians per second.
w = 1047radians per second
Kinetic energy needed is ½ I w w = ½ x 3.25 x 1047 x 1047 x 10 ^(-2)= 17813 joule.

Answer 4

The energy is 1/2 I omega^2.

Here omega is measured in radians per second. To get from rpm to radians per second, multiply with 2 pi and divide by 60.
Now the rest should not be too difficult.

Answer 5

I did not understand the moment of inertia u wrote what value is it anyways the energy required is 1/2(I*w*w)
where I :->Moment of iertia
w :->angular velocity...1000rpm in this case.....

Answer 6

Check the equation from some physics book and solve the problem. That's how real physicists do it.

Answer 7

Ur Home work????????