(40 points) Consider a lollipop that\'s rotating and the axis of rotation is per

Question

(40 points) Consider a lollipop that's rotating and the axis of rotation is perpendicular to the plain of candy. If the mass of the stick is Ms and its length is L, and the radius of the candy is R and mass is Mc a) (5 points) what is the moment of inertia of the thin rod around the axis crossing its center of mass and perpendicular to itself? b) (5 points) What is the moment of inertia of the candy disk around the axis crossing its center of mass and perpendicular to the disk? c) (5 points) What is the Parallel Axis Theorem? d) (10 points) What is the lollipop's moment of inertia when it rotates around the triangular dot? e) (15 points) What is the lollipop's moment of inertia when it rotates around the circular dot (at the top-edge of the candy)?

Explanation / Answer

a)

I = Ms L^2 /12

b)

McR^2/2

c)

Parallel axis theorem gives the value of moment of inertia about any axis other than the centroidal but parallel to it

I = Ig + Mr^2

d)

Using Parallel axis theorem

r = R+L

I = Ig + Mcr^2

= McR^2/2 + Mc(R+L)^2

= Mc (R2/2 + R2 + 2RL + L2)

  

e)

Again using parallel axis theorem

I = Ig + Mcr^2

= McR^2/2 + McR^2

= 3McR2/2

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