Question

A rigid body is made of three identical thin rods, each of length L fastened together in the form of letter H. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body is allowed to fall from rest from a position in which the plane of H is horizontal. What is the angular speed of the body when the plane of H is vertical?

• A.
• B. $\frac { 1 } { 2 }$
• C. $\frac { 3 } { 2 }$
• D. 2

Answer 1

Answer: (C)

$\frac { 3 } { 2 }$

Answer 2

I = 0 + $\left[ \frac { \mathrm { ML } ^ { 2 } } { 12 } + \mathrm { M } \left( \frac { \mathrm { L } } { 2 } \right) ^ { 2 } \right]$+ [0 + ML²] = $\frac { 4 } { 3 }$ML²

Q $\frac { 1 } { 2 }$Iw² = mgh_{CM ;} \ =$3 \mathrm { Mg } \left( \frac { \mathrm { L } } { 2 } \right)$

Þ w = $\frac { 3 } { 2 } \sqrt { \frac { \mathrm {~g} } { \mathrm {~L} } }$