Rigid body dynamics problem

[Goodwill]

Homework Statement

A uniform solid cube of edge length 2a is suspended from a horizontal axis along one edge. find the length of the equivalent simple pendulum. given that the cube is released from rest with

Relevant Equations

I = Icm + Md*d

I

 

[BvU]

Hello @Goodwill ,

Please complete your post and add your best attempt. And your question ...

$\$

 

[Goodwill]

Hello @Goodwill ,

Please complete your post and add your best attempt. And your question ...

$\$

 

[Goodwill]

Attached a solution, please check

 

[Lnewqban]

Attached a solution, please check

Welcome, Goodwill!
No attachment is visible.

 

[Goodwill]

Welcome, Goodwill!
No attachment is visible.

 

[Goodwill]

 

[BvU]

What is your question?

Please have pity on us helpers and observe
https://www.physicsforums.com/threads/homework-help-guidelines-for-students-and-helpers.686781/

 

[Goodwill]

Question
A uniform solid cube of edge length 2a is suspended from a horizontal axis along one edge. find the length of the equivalent simple pendulum. given that the cube is released from rest with its centre of mass level with the axis, find is angular velocity when it reaches the lowest point

 

[Lnewqban]

Please, see:
https://en.wikipedia.org/wiki/Pendulum#Compound_pendulum

https://www.schoolphysics.co.uk/age16-19/Mechanics/Rotation of rigid bodies/text/Compound_pendulum/index.html#:~:text=Since the formula for a simple pendulum is,L = [k 2 + h 2 ]/h

https://en.wikipedia.org/wiki/List_of_moments_of_inertia

 

[PeroK]

Question
A uniform solid cube of edge length 2a is suspended from a horizontal axis along one edge. find the length of the equivalent simple pendulum. given that the cube is released from rest with its centre of mass level with the axis, find is angular velocity when it reaches the lowest point

Your diagram above appears to show a vertical axis. As I understand the question, the cube is swinging backwards and forwards under gravity.

 

[Goodwill]

Your diagram above appears to show a vertical axis. As I understand the question, the cube is swinging backwards and forwards under gravity.

I couldn't draw it upside down but it just a illustration how the system moves

,

 

[Lnewqban]

 

[haruspex]

One of the problems with posting images of working, in violation of the guidelines, is that others cannot easily reference specific lines in it.

In your energy conservation equation, how do you get $\frac 43\sqrt 2$ for the vertical displacement?