Year 12 EPI: All help immensely appreciated

[kushwoho44]

This is an excerpt from my EPI (It's a SAC worth 40 mark/100marks for the semester) so am being super super pedantic. Was just wondering if anyone could proof read it and make sure I have explained myself well:



The moment of inertia is a principle that measures an object’s resistance to changes in rotation. In the case of cantilever beams, the moment of inertia can be used to calculate the deflection of the beam when combined with a ‘Force Vs Deflection’ formula. The axis of rotation will be taken at the position of the clamp. The moment of inertia can be used to relate force and deflection by the formula:
F =       where F=Force (N), E= Elastic modulus of the material (Pa),
 w= Width of the beam (m), t= Thickness of the beam (m),L= Length of the beam (m) and d= Deflection in the beam (m). This means that the further we move our mass from the clamp, the greater the moment of inertia and the greater our mass, the greater the moment of inertia. It also means that a beam of greater breadth will require a greater force for the same displacement as in a narrower beam.

[schnappy]

You clearly need to do some reading on what the moment of inertia is. It isn't a 'principle' it's a quantified value, it depends on where the center of rotation is ('pivot point' if you like) and the mass of the object and how that mass is distributed. The moment of inertia does not increase as you move your mass out, the torque being applied to the beam does however increase, since Torque = Fr, r is proportional to torque hence an increase in r will result in an increase in torque. F = mg, which is constant I assume.

The moment of inertia is its resistance to rotation, in the EXACT same way that mass is the resistance to a change in motion. If you take any newtonian mechanics equation and you see acceleration, mass, velocity and position you can just substitute those for angular position, angular acceleration, angular velocity and moments of inertia in place of mass. Intuitively, the heavier something that is rotating it is, the harder it is to change its rotational motion yes? Yes of course, so part of the moments of inertia is mass. Moments of inertia are denoted by I, where I = mrr^2 nominally (It's actually integral(r^2 dm)). You can then use the parallel axis theorem to find the moments of inertia about a symmetrical object given the moments of inertia in the center, though since you're dealing with it at the end it's a bit simpler - just google for moments of inertia calculations and find the one applicable to your scenario.

This is all above VCE level, so you don't need to really look into it. But your definition is wrong.