Calculating Torque & Forces - Solve It Now

[mathildej]

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?

 

[Hootenanny]

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?

 

[Moetasim]

I would approach this problem by breaking it down into smaller components and using known equations and principles to solve for the torque of air resistance on the two connected balls.

First, I would start by defining the variables and parameters given in the problem. This includes the force due to air resistance (Fk), angular velocity (w), velocity of the center of mass (Vcm), mass of each ball (M), radius of each ball (R), a constant (Kv), torque (T), moment of inertia in the center of mass (Icm), and moment of inertia for each ball (Ia and Ib).

Next, I would consider the forces acting on the system. In this case, we have the force of gravity pulling the balls down, and the force of air resistance acting in the opposite direction. Since the balls are rotating around the center of mass, there is also a torque acting on the system due to air resistance.

To find the torque of air resistance, I would use the equation T = r x F, where r is the position vector from the center of mass to the point where the force is applied, and F is the force applied. In this case, the force of air resistance is acting on each ball, so we can calculate the torque on each ball separately and then add them together to get the total torque.

To calculate the torque on each ball, we need to find the position vector (r) and the force of air resistance (Fk). The position vector can be found using the radius of each ball (R), and the distance from the center of mass to the center of each ball (r). The force of air resistance can be calculated using the given equation Fk = -2Kv * Vcm.

Once we have the torque on each ball, we can add them together to get the total torque on the system. Since the balls are connected, we can assume that the total torque is equal to the torque on one ball multiplied by two.

Finally, we can substitute the values for the given variables and solve for the torque of air resistance. This should give us the answer of T = -2Kv * w * R^2.

In summary, as a scientist, I would approach this problem by breaking it down into smaller components, using known equations and principles, and carefully considering the forces and torques acting on the system. By following this methodical approach, we can arrive at the correct solution for