# How to find angular velocity from torque?

Hello,

If I apply force on a rigid cube, I can find the torque τ as:

τ = F x r

Now, from torque τ I can know about the axis of rotation but how much should I rotate the cube. How can I find the angular velocity ω from torque τ? Or is there any other way by which I can find how much the object rotates every second?

Thank you.

SteamKing
Staff Emeritus
Homework Helper
What do the equations of angular motion tell you?

What do the equations of angular motion tell you?

The angular velocity will tell me the velocity with which I should rotate the cube. Is there anyway I can find it with the help of torque?

SteamKing
Staff Emeritus
Homework Helper
If you study the equations of angular motion, you'll see that for a body rotating with a constant angular velocity, there is no net torque applied.

It's analogous to a spaceship travelling at a constant linear velocity: there is no net force being applied to the spaceship.

Force and torque accelerate objects from one velocity to another, so when these are applied, the velocity is always changing.

So, how do I find the amount by which I should rotate an object every second if I know the torque of an object?

SteamKing
Staff Emeritus
Homework Helper
You can calculate the amount of torque required to accelerate the object, say from rest to a certain angular velocity.

Your question is a bit unclear. If you want to determine what the angular velocity of a rotating object, that can be accomplished by using a stroboscope or timing light.

You can calculate the amount of torque required to accelerate the object, say from rest to a certain angular velocity.

Your question is a bit unclear. If you want to determine what the angular velocity of a rotating object, that can be accomplished by using a stroboscope or timing light.

What I mean is I have an object lying in the 3D space. If I apply a certain force, how do I find the axis on which it should rotate and how much amount the object should rotate depending on the force applied and the duration of the force applied?

Hello,

If I apply force on a rigid cube, I can find the torque τ as:

τ = F x r

Now, from torque τ I can know about the axis of rotation but how much should I rotate the cube. How can I find the angular velocity ω from torque τ? Or is there any other way by which I can find how much the object rotates every second?

Thank you.

we know
(torque) = (moment of inertia).(angular acceleration)

ζ=Iα

also
α = dω/dt

or

dω/dt= ζ/I

and at last

ω = (ζ)/(I) . dt

even if ζ is time dependent calculate ω,
[caution do not forget integration constant i.e. initial angular velocity]

ζ=Fxr

put it in the integrating equation

D H
Staff Emeritus
This is fine for a cube because the momentum of inertia of a cube, like a sphere, can be treated as a scalar. This is not true in general. The moment of inertia is tensorial in nature. If you don't know what that means, that's okay if this is for a lower level (freshman/sophomore level or below) physics class. Those lower level physics classes steer clear of cases where this tensorial nature rears its ugly head.

This is fine for a cube because the momentum of inertia of a cube, like a sphere, can be treated as a scalar. This is not true in general. The moment of inertia is tensorial in nature. If you don't know what that means, that's okay if this is for a lower level (freshman/sophomore level or below) physics class. Those lower level physics classes steer clear of cases where this tensorial nature rears its ugly head.
when does this level come
Phd!!!
mann! you are awesome at vocab:tongue: and physics

D H
Staff Emeritus