Angular kinetics

Question

Suppose a long bone is idealized as a solid cylinder with a diameter of 0.03 m. During a torsion test, if the torsion moment is 10N.m, what is the maximal stress caused by torsion? (Hint: polar moment of inertia of the cross-sectional area is equal to π r4/2 , π = 3.14, r is the radius).

Answer 1

The maximal stress caused by torsion can be found using the equation:

τ = T*r/J

Where:

τ (tau) = the maximum stress caused by torsion,

T is the applied torque,

r is the distance to the outermost point, in this case the radius,

J is the polar moment,

For a solid cylinder, the polar moment is equal to that of a solid circle and can be found usingτ:

J = π*r⁴/2

This yields a final equation of:

τ = 2*T/(π*r³)

Taking the diameter of 0.03m yields a radius of 0.015m, and substituting in to the equation above in addition to T = 10Nm leads to a maximum stress of ~1.886 MPa.