Question

Imagine a scenario where you have a hollow cylinder and you press this hollow cylinder down onto some surface (lets imagine its in the x-y plane) such that it is not rolling but its cross section is flat against the surface. You have a friend that comes by and tries to rotate this cylinder (around the z-axis) from underneath you while you are pressing down. How can you calculate how big the moment around z needs to be to rotate this hollow cylinder given the axial force being used to push down onto this cylinder?

Answer 1

To calculate the torque needed to rotate a hollow cylinder, you need to consider the moment of inertia and use Newton's second law for rotation.

When calculating the moment around the z-axis needed to rotate a hollow cylinder, you need to consider both the axial force being used to push down onto the cylinder and the moment of inertia of the cylinder. The moment of inertia of a hollow cylinder can be calculated using the formula I = ½M(R_outer² + R_inner²), where M is the mass of the cylinder, R_outer is the outer radius, and R_inner is the inner radius. Once you have the moment of inertia, you can use Newton's second law for rotation, τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration. Rearranging this equation, you can calculate the torque needed to rotate the cylinder around the z-axis.

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