Two rotating wheels have masses such that m2 = 5 m1, and radii such that R2 = 4 R1. If the angular accelerations of the wheels are equal, then what is the relationship between the two forces.

F2 = 20 F1 F2 = 5 F1 F2 = 16 F1 None of the above

What is the relationship between the torques? t2 = 25 t1 t2 = 80 t1 t2 = 5 t1 t2 = 20 t1

What forces?

never mind i got the answer

thanks anyway

To determine the relationship between the forces and torques in this scenario, we can use the principles of rotational motion and torque.

First, let's consider the relationship between the forces applied to the rotating wheels. The net torque acting on an object is given by the equation:

τ = I * α

Where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

For a rotating object, the moment of inertia is proportional to both the mass and the square of the radius. So we can write:

I = m * R^2

Where m is the mass and R is the radius.

In this case, let's assume that the angular accelerations of the wheels are equal, denoted as α1 and α2 for the first and second wheels respectively.

Given that m2 = 5 m1 and R2 = 4 R1, we can substitute these values into the equation for the moment of inertia:

I1 = m1 * R1^2
I2 = m2 * R2^2

Since α1 = α2, we can equate the torques for the two wheels:

τ1 = I1 * α1
τ2 = I2 * α2

Substituting the expressions for the moments of inertia:

τ1 = (m1 * R1^2) * α1
τ2 = (m2 * R2^2) * α2

Dividing the equations for τ2 and τ1:

τ2 / τ1 = [(m2 * R2^2) * α2] / [(m1 * R1^2) * α1]

Simplifying the equation:

τ2 / τ1 = (m2 * R2^2) / (m1 * R1^2)

Substituting the given values:

τ2 / τ1 = ((5 * m1) * (4 * R1)^2) / (m1 * R1^2)
= (5 * m1 * 16 * R1^2) / (m1 * R1^2)
= 80

Therefore, the relationship between the torques is t2 = 80 * t1.

To summarize:
- The relationship between the forces is F2 = 20 * F1.
- The relationship between the torques is t2 = 80 * t1.