How to find angular velocity from torque?

In summary, the angular velocity tells you how fast the object should rotate. You can find this by using a stroboscope or timing light.
  • #1
geekie weekie
7
0
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.
 
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  • #2
What do the equations of angular motion tell you?
 
  • #3
SteamKing said:
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?
 
  • #4
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 traveling 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.
 
  • #5
So, how do I find the amount by which I should rotate an object every second if I know the torque of an object?
 
  • #6
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.
 
  • #7
SteamKing said:
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?
 
  • #8
geekie weekie said:
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]

as per your question


ζ=Fxr

put it in the integrating equation
 
  • #9
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.
 
  • #10
D H said:
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
 
  • #11
It's the second or third year in college where one learns that moment of inertia is a tensor rather than a scalar. With regard to grammar, get in the habit of writing complete sentences. It's a rule of this site, and it's also a rule in life beyond college.
 
  • #12
d h said:
it's the second or third year in college where one learns that moment of inertia is a tensor rather than a scalar. With regard to grammar, get in the habit of writing complete sentences. It's a rule of this site, and it's also a rule in life beyond college.

ohh yeah i was told this i just remember tenser told to me in 7th
like current is tensor quantity which is having some direction (lol! I don't know exactly but yeah i want to ask is time also tensor quantity)
i when studied electricity at coaching at beginning of my 9th this year i opposed teacher by saying example of time but not confirm
 

1. What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates around a fixed point. It is usually expressed in radians per second (rad/s) or revolutions per minute (rpm).

2. How is angular velocity related to torque?

Angular velocity and torque are related through the equation: angular velocity = torque / moment of inertia. This means that the angular velocity of an object is directly proportional to the torque applied to it and inversely proportional to its moment of inertia.

3. How do I calculate angular velocity from torque?

To calculate angular velocity from torque, you need to know the value of the torque applied to the object and its moment of inertia. You can then use the equation mentioned above: angular velocity = torque / moment of inertia.

4. Can I use any unit for torque and moment of inertia when calculating angular velocity?

Yes, you can use any unit for torque and moment of inertia as long as they are consistent. For example, if you use newton-meters (N·m) for torque, you should use kilograms squared per meter squared (kg·m^2) for moment of inertia.

5. How does angular velocity affect the motion of an object?

Angular velocity affects the motion of an object by determining how quickly it rotates around a fixed point. Objects with higher angular velocity will rotate faster, while objects with lower angular velocity will rotate slower. Additionally, changes in angular velocity can also affect the stability and direction of an object's motion.

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