Calculating Torque & Forces - Solve It Now

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SUMMARY

The discussion focuses on calculating the torque of air resistance for two connected balls falling through air and rotating around their center of mass. The key equation derived is T = -2Kv * w * R^2, where T represents torque, Kv is a constant related to air resistance, w is the angular velocity, and R is the radius of each ball. The moment of inertia for each ball is given by Ia = Ib = (2/5)MR^2, and the force due to air resistance is expressed as Fk = -2Kv * Vcm. The user seeks assistance in deriving the correct torque equation based on these parameters.

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  • Knowledge of air resistance forces
  • Basic principles of rotational dynamics
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  • Learn about the effects of air resistance on falling objects
  • Explore the relationship between angular velocity and torque
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Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators seeking to explain the concepts of torque and air resistance in rotational motion.

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Homework Statement


Two balls are connected together and fall through air. They also rotate around the center of mass. I'm supposed to find an equation for the torque of air resistance through the center of mass.
Fk= Force due to air resistance on each of the balls
w=angular velocity
Vcm=velocity of the center of mass
M=mass of each ball
R=radius of each ball
Kv=constant
T=torque
Icm=moment of inertia in the center of the mass
Ia=Ib= moment of inertia for each ball
r= position of the ball relative to the center of mass

Homework Equations


Ia=Ib=(2/5)MR^2
Fk=-2Kv*Vcm
Icm=(14/5)M(R^2)
Va=Vcm+w X r
Vb=Vcm - w X r
This is the answer I'm supposed to get: T=-2Kv*w*R^2

The Attempt at a Solution


I have tried sooo many different ways to get this.
And still I have no idea. Can anyone help me?
 
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mathildej said:
I have tried sooo many different ways to get this.
And still I have no idea. Can anyone help me?
Hi mathildej and welcome to PF,

Would you mind detailing some of the methods you have tried?
 

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