Hollow rod vs solid rod; which one is easier to twist?

[Fanghur]

Let's say we have two rods/bones/whatever, that are the same length and mass. And let's say that one of the rods is solid and the other one is hollow.

 

Can someone explain to me why it is that it's easier to twist (i.e. shear forces) the solid rod than it is the hollow one? That seems completely counter-intuitive. And also, just correct me if I am mistaken here; since the solid one is easier to twist, that would also mean that its angle of shear (i.e. θ) would be greater than the θ of the hollow rod, right?

 

This concept is driving me mad, someone please help me.

[swansont]

If one is hollow and the other solid, with the same mass, then they do not have the same radius (or they are not made of the same material).

[Fanghur]

Swansont, what you just said was implicit in how I worded my question, what I need is why? Why are hollow bones more resistant to torsional strain than solid bones would be? Why would it be easier to twist a solid bone than it would be to twist a hollow bone?

[InigoMontoya]

Swansont, what you just said was implicit in how I worded my question, what I need is why? Why are hollow bones more resistant to torsional strain than solid bones would be? Why would it be easier to twist a solid bone than it would be to twist a hollow bone?

If the solid bone was of the same radius as the hollow bone, it would indeed be more difficult to twist. But by your requirement for same length and mass the radius is not the same. As such, the hollow bone will be more difficult to twist. As for why... Basically the resistance to torsion of a rod is related to the 4th power of it's radius. Smaller radius? Radically smaller ability to resist torsion. For more information, see: Polar moment of inertia.

Edited March 1, 2011 by InigoMontoya

[forufes]

Swansont, what you just said was implicit in how I worded my question, what I need is why? Why are hollow bones more resistant to torsional strain than solid bones would be? Why would it be easier to twist a solid bone than it would be to twist a hollow bone?

because it's easier to twist this than to twist this .

even in the solid bone, the closer you get to the core the less torque the material is withstanding [stress].

because stress here is a function of torque, and torque is a function of the arm length, which here is the radius.

if the hollow and solid bones had the same radius then the solid one would resist slightly more torque.