@JohnRennie Hi :-)

@Knight hi :-)

@JohnRennie Sir why a rigid body rotating With constant speed doesn’t need an external force to keep it up. Rotation of particles other than CM does change their velocity with time, but people say this change in velocity is taken care by internal forces only

Isn't that obvious? If $\alpha = 0$ then the torque is zero i.e. thre are no external forces.

What’s $\alpha$ ?

@JohnRennie

$\alpha$ is the usual symbol for angular acceleration i.e. $\alpha = d\omega/dt = d^2\theta/dt^2$

So $\alpha = 0$ means constant angular velocity

@JohnRennie But theta does change with time, isn’t it?

Let’s take a wheel rotating around CM, then the particle at rim is revolving and it’s angle is changing with time

$d\theta/dt \ne 0$ yes, but $d^2\theta/dt^2$ does equal zero.

It's like at constant velocity $dx/dt \ne 0$ but the acceleratin $d^2x/dt^2$ is zero.

Yes

I agree

But for the particle at rim we have $$\frac{dv}{dt} \neq 0$$

Only the direction changes, not the magnitude, so while there is a centripetal force it is doing no work so the KE of the particle doesn't change.

Yes I agree

$$\vec F = m \frac{d\vec v}{dt}$$ And $$\frac{d\vec v}{dt} \neq 0$$ therefore, there does exist a force.

I need to go now I'm afraid.

I'll be back later or tomorrow morning.

Okay sir

@JohnRennie Sir What did you mean by “isolated”? Did you mean no “external force” ?

@Knight Yes

@JohnRennie How are you?

You’re cute and loving

@Knight Good thanks, how are you?

@JohnRennie Healthy and fine

Sir please explain me with some real life example how can a body rotate without any external force

The Earth rotates without an external force

Really? I didn’t know that (no kidding)

This such an elementary subject that I wonder if I have misunderstood what you are asking about.

Angular momentum is conserved unless an external torque is acting.

Yes

Just like linear momentum is conserved unless an external force is acting.

No external force means no external torque, so the angular momentum is conserved.

Rotation involeves change of linear momentum.

Suppose you are whirling a stone round on the end of a string.

And we'll assume this is frictionless

Then the angular momentum of the stone is constant. Yes?

Yes he he he he he he

The linear momentum is indeed changing, and that is because the tension in the string exerts a force on the stone that changes its linear momentum.

But since that force passes through the centre of rotation that force produced no torque.

Yes, $\mathbf F \times \mathbf r$

So the stone is another example of constant angular velocity because no external torque is acting.

Wow! No torque and then also we got a rotation. God !

You had to apply a torque to get the stone whirling round, and you need to apply a torque to slow it down again, but no torque is needed when the stone is moving at constant angular velocity.

Thank you so much sir, really thank you

@Knight you're welcome :-)

But isn't this basic mechanics?

@JohnRennie My problem was that a changing linear momentum needs a force, but when you said “isolated” I thought no force at all. Did I get you correctly?

The force that changes the linear momentum is an internal force i.e. the material that the body is made from exerts the force.

Like the tension in the string for our whirling stone.

Okay

Internal force means momentum is decreasing somewhere in the system and increasing somewhere else in the system, hence no net change, ha?

Remember that because momentum is a vector a change in its direction is a change even is the magnitude of the vector is constant.

Typically in circular motion the internal forces cause a change in the direction of the linear momentum but its magnitude is constant.

So I'm not sure I would say "momentum is decreasing somewhere in the system and increasing somewhere else in the system"

Okay. Can you please explain how in that string and stone example how change in momenta cancel each other?

A simpler example would be two stones of equal masses at both ends of a string and whirling around each other.

Yes, change in momenta are completely in different directions

I meant opposite