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.
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?
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?
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?
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
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.
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 7^{th} like current is tensor quantity which is having some direction (lol! I dont know exactly but yeah i wanna ask is time also tensor quantity) i when studied electricity at coaching at beginning of my 9^{th} this year i opposed teacher by saying example of time but not confirm