Question

Rotational Motion. pls help me check my answers! :D

Answer 1

a.) \[I _{s}= \frac{ 1 }{ 2 }M _{1}R _{1}^2\]
\[I _{p}=M _{2}R _{2}^2+M _{2}R _{2}^2= 2M _{2}R _{2}^2\]
\[I _{s}+I _{p}=\frac{ 1 }{ 2 }M _{1}R _{1}^2+2M _{2}R _{2}^2\]

b.) By parallel axis theorem and perpendicular axis theorem,

\[I _{h}= M _{3}L^2 + I'_{h}\]
\[I'_{h}=2 \times I''h\]
I'h -> moment of inertia of hoop about vertical axis which passes through the centre of the hoop
I''h -> moment of inertia of hoop about axis perpedicular to the hoop which passes through its centre.
\[I'_{h}=2M _{3}R _{3}^2\]
\[I _{h}= M _{3}L^2+2M _{3}R _{3}^2\]
\[L _{h}=M _{3}\omega _{0}(L^2+2R _{3}^2)\]

direction will be counter-clockwise.

c.) L (initial) = L(final)

\[0 + M _{3}\omega _{0}(L^2+2R _{3}^2)= M _{3}\omega _{2}(L^2+2R _{3}^2)+ \frac{ 1 }{ 2 } M _{1}\omega _{1} R _{1}\]

KErot. (initial) = KErot. (final)
\[\frac{ 1 }{ 2 }M _{3}\omega _{0}^2(L^2+2R _{3}^2)+0 = \frac{ 1 }{ 4 }M _{1}R _{1}^2\omega _{1}^2+ \frac{ 1 }{ 2 }M _{3}\omega_{2}^2(L^2+2R _{3}^2)\]

Answer 2

yes girl you are right
but i think you need to check the angular momentum conservation equation (the moments of inertia) and also the energy conservation equation
maybe