Question

What is the moment of inertia of the wheel?

Answer 1

A) .026 kg*m^2
B) .023 kg*m^2
C) .034 kg*m^2
D) .046 kg*m^2
E) .020 kg*m^2

Answer 2

C

Answer 3

How you get that?

Answer 4

Actually I believe the answer is A. If you draw a free body diagram, you'll find there are two forces acting: the force generated by the mass and one opposing it that is creating torque around the wheel. In equation form that would be this:\[F _{net}=F _{mass}-F _{torque}\]Torque is given by the following:\[T=I \alpha=Fr\]where T is torque;I is the moment of inertia; alpha is the angular acceleration of the wheel; F is the force creating torque on the wheel; and r is the radius of the wheel. So we can now get, via manipulation, the force creating the torque:\[F _{torque}=\frac{ I \alpha }{ r}=\frac{ Ia }{ r ^{2} }\]where a is the tangential acceleration experienced by the wheel (5m/s^2). This is the result of the following relationship:\[a _{tangential}=\alpha r\]Now inserting what we know now into the force equation I gave (first equation) we get:\[ma=mg-\frac{ Ia }{ r ^{2} }\]You then solve that last equation for I.

Answer 5

When I run the above through my calculator I get I=0.02592≈0.026

Answer 6

Thank you so much!