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Action and Reaction in Rotation
Storyboard

Newton's third principle in the case of rotation defines that the torques have to be generated in pairs so that their sum is zero. This implies that before an action there is always a reaction of equal magnitude but in the opposite direction.

>Model

ID:(757, 0)


Action and reaction in torque
Image

Similar to the case of translational motion, where the third principle states that every action has an equal and opposite reaction. This means that if I try to rotate an object in one direction, its support will rotate in the opposite direction.

An example of this is a rotating chair. This exercise can be done with extended legs and arms, attempting to rotate in the same direction, or with an object that is rotating and an attempt to alter its angular momentum, which generates an opposing angular momentum in the support:

.

ID:(10291, 0)


Action and Reaction in Rotation
Model

Newton's third principle in the case of rotation defines that the torques have to be generated in pairs so that their sum is zero. This implies that before an action there is always a reaction of equal magnitude but in the opposite direction.

Variables
Symbol
Text
Variable
Value
Units
Calculate
MKS Value
MKS Units
$I_1$
I_1
Moment of inertia of the first object
kg m^2
$I_2$
I_2
Moment of inertia of the second object
kg m^2
$T_R$
T_R
Reaction Torque
N m
$\Delta t$
Dt
Time elapsed
s
$T_A$
T_A
Torque Action
N m
$\Delta\omega_1$
Domega_1
Variation of angular velocities of the first object
rad/s
$\Delta\omega_2$
Domega_2
Variation of angular velocities of the second object
rad/s
$\Delta L_1$
DL_1
Variation of the angular momentum of the first object
kg m^2/s
$\Delta L_2$
DL_2
Variation of the angular momentum of the second object
kg m^2/s

Calculations

First, select the equation:   to ,  then, select the variable:   to 
Symbol
Equation
Solved
Translated

Calculations

Symbol
Equation
Solved
Translated

 Variable   Given   Calculate   Target :   Equation   To be used


Equations

Since action and reaction in the case of forces are given by

$ F_R =- F_A $



multiplying this equation by the radius yields

$rF_R=-rF_A$



and with

$ T = r F $



we have

$ T_R = - T_A$

.

(ID 11006)

Examples


(ID 15839)

Similar to the case of translational motion, where the third principle states that every action has an equal and opposite reaction. This means that if I try to rotate an object in one direction, its support will rotate in the opposite direction.

An example of this is a rotating chair. This exercise can be done with extended legs and arms, attempting to rotate in the same direction, or with an object that is rotating and an attempt to alter its angular momentum, which generates an opposing angular momentum in the support:

.

(ID 10291)


(ID 15836)

ID:(757, 0)