How Is Net Torque Calculated on a Rotating Sphere?

[mathdude88]

Homework Statement

see problem 4 attachment

Homework Equations

see problem 4 attempt attachment

The Attempt at a Solution

see problem 4 attempt attachment

 

[PhanthomJay]

You started out correctly by determining the angular acceleration, but then you reverted back to translational motion using F=ma. What's the form of Newton 2 applied to rotating objects that are accelerating?

 

[thomate1]

The net torque on a sphere can be calculated using the formula τ = Iα, where τ is the net torque, I is the moment of inertia, and α is the angular acceleration. In this problem, the sphere is rotating about its center of mass, so the moment of inertia can be calculated as I = 2/5mr^2, where m is the mass of the sphere and r is its radius. The angular acceleration can be determined by dividing the angular velocity by the time interval. Once these values are known, the net torque can be calculated and its direction can be determined using the right-hand rule. It is important to note that the net torque on a sphere will always cause it to rotate about its axis, and the direction of rotation will depend on the direction of the net torque. This calculation is crucial in understanding the rotational motion of objects and can be applied to various real-world scenarios, such as the motion of planets in our solar system or the spinning of a top.