# What is Rotation inertia torque: Definition and 12 Discussions

In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment, moment of force, rotational force or turning effect, depending on the field of study. The concept originated with the studies by Archimedes of the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object around a specific axis. Another definition of torque is the product of the magnitude of the force and the perpendicular distance of the line of action of a force from the axis of rotation. The symbol for torque is typically

τ

{\displaystyle {\boldsymbol {\tau }}}
or τ, the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the point about which the torque is being measured to the point of force application, and the angle between the force and lever arm vectors. In symbols:

τ

=

r

×

F

{\displaystyle {\boldsymbol {\tau }}=\mathbf {r} \times \mathbf {F} \,\!}

τ
=

r

F

sin

θ

{\displaystyle \tau =\|\mathbf {r} \|\,\|\mathbf {F} \|\sin \theta \,\!}
where

τ

{\displaystyle {\boldsymbol {\tau }}}
is the torque vector and

τ

{\displaystyle \tau }
is the magnitude of the torque,

r

{\displaystyle \mathbf {r} }
is the position vector (a vector from the point about which the torque is being measured to the point where the force is applied),

F

{\displaystyle \mathbf {F} }
is the force vector,

×

{\displaystyle \times }
denotes the cross product, which produces a vector that is perpendicular to both r and F following the right-hand rule,

θ

{\displaystyle \theta }
is the angle between the force vector and the lever arm vector.The SI unit for torque is the newton-metre (N⋅m). For more on the units of torque, see § Units.

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1. ### A Order of rotations due to torque in 3DOF in simulations

Hi, I am running a computational fluid dynamics (CFD) simulation. Supposed I have a symmetrical rigid body in space experiencing torque in the global x,y,z axes. It is stationary at t = 0. I also constrain it to only allow rotations in 3DOFs, and no translation. It will rotate and I need to...
2. ### Forces when car wheels "lay rubber"

Suppose the car is moving to the right, so if the wheels roll without slipping, they are rolling clockwise. To get the wheel to slip, a counterclockwise torque would need to be applied to cause the wheel to have some angular acceleration. If the wheel was slipping, then the bottom of the wheel...
3. ### I Changing the RPM of a frictionless spinning wheel in a box

Imagine a spinning wheel built into a hand size vacuum box. There is no friction between the axe bearings of the wheel and the box. Let's say that the wheel rotates with 60 RPM. Am I right if I assume: 1. The wheel continues to rotate, approximately as if in space. 2. It is not possible to...
4. ### Is the AP Physics 1 textbook flawed in its explanation of moment of inertia?

Homework Statement [/B] I'm probably missing something basic here but: The moment of inertia of a body does NOT depend on which of the following? (choose 2 answers) A: The angular acceleration of the body B. The distribution of mass in the body C. The angular velocity of the body D. The axis...
5. ### Rotational Mechanics Question.

Homework Statement A tangential force F acts at the top of a thin spherical shell of mass m and radius R. Find the acceleration of the shell if it rolls without slipping. Homework Equations Since the shell is rolling, friction does not act at the bottom. So equating the torque, F*R= I*α The...
6. ### Where is wrong in this proof for rotational inertia ?

Homework Statement Prove the formula for inertia of a ring (2D circle) about its central axis. Homework Equations I = MR^2 Where: M: total mass of the ring R: radius of the ring The Attempt at a Solution - So I need to prove the formula above. - First, I divide the ring into 4...
7. ### Center of percussion of a baseball bat

Homework Statement A baseball rests on a frictionless, horizontal surface. The bat has a length of 0.900m, a mas of 0.800kg, and its center of mass is 0.600m from the handle end of the bat (see figure below). The moment of inertia of the bat about its center of mass is 0.0530 kg.m^2. The bat is...
8. ### Calculation of torque to stop a wheel.

Homework Statement A wheel of moment of inertia 5×10-3kg-m2 is making 20 rev/s. Find the torque required to stop it in 10s is (A) 2π×10-2Nm (B) 2π×102Nm (C) 4π×10-2Nm (D) 4π×102Nm Answer - (A). Homework Equations ω=2πƒ (ƒ=frequency) Power (P) = Γω. P = W/t. W = ΔK.E. = (1/2)Iω2. The...
9. ### How to simulate rotational stability of multiple parts?

I've written a space colony simulation game called High Frontier. It correctly simulates rotational stability when most of the mass is dominated by a single large spinning part. For example, a squat cylinder will be stable, but a long cylinder will end up tumbling end over end, as shown...
10. ### Clay-stick inertia & energy problem

Homework Statement A thin stick of mass M = 2.8 kg and length L = 2.2 m is hinged at the top. A piece of clay, mass m = 0.8 kg and velocity V = 2.7 m/s hits the stick a distance x = 1.65 m from the hinge and sticks to it. Q2: What is the ratio of the final mechanical energy to the initial...
11. ### Atwood's machine with two connected discs

Homework Statement The system looks like this: I have two discs which are connected. Disc 1 has ##R_1##(radius) and ##M_1##(mass) Disc 2 has ##R_2## and ##M_2## ## R_2 > R_1 ## ## M_2 > M_1 ## on both discs weights are attached on opposite sides. On smaller ##m_1## is pulling and on bigger...
12. ### Cylinder rolling thanks to external torque.

Homework Statement A cylinder of mass m and radius R is set on a plane, with large enough friction coefficient to ensure at any moment rolling without slipping. A constant torque is applied along the axis passing through the center of mass (G) of the cylinder and perpendicular to the basis of...