KE of a bar rotating at an angle

[chiralvandal]

KE of a bar rotating at an angle- please help!

Homework Statement

A slender prismatic bar DE Of length l(=1 m) and weight W(= 89 N) is rigidly attached at it's midpoint C to a shaft AB and makes an angle (alpha(=45degrees)) as shown in the figure. Find the kinetic energy T of the bar if it rotates with constant angular velocity (omega(=200 rpm)) about AB.

Homework Equations

Work done= change in KE

and

Work done= integration of moments about the axis of rotation

The Attempt at a Solution

I'm supposed to use the work- energy relation to solve this question but am clueless as to how to go about it... please help!

 

[Mentz114]

You need to find the moment of inertia of the slender rod about the axis. There is a formula that connects the kinetic energy to the MoI and the angular velocity ( omega). Have a look at this, down the page to rotational KE.

http://en.wikipedia.org/wiki/Kinetic_energy

 

[chiralvandal]

thanks for replying!
the problem is i don't know how to get the moment of inertia... should i assume the bar to be two rotating cones or something like that?
and after i get this, should i also include translation to find the energy?

 

[Mentz114]

In general, the MoI of a mass m rotating a distance r from its axis is m*r^2.

Work out the center of gravity for each arm, then use the perpendicular distance from the center of mass to the axis to get the MoI of each side.

There's no translational energy, I think.

 

[stunner5000pt]

thanks for replying!
the problem is i don't know how to get the moment of inertia... should i assume the bar to be two rotating cones or something like that?
and after i get this, should i also include translation to find the energy?

are you supposed to derive the monent of inertia or are you allowed to look up the formula??

if ou allowed to look it up then go here
http://en.wikipedia.org/wiki/List_of_moments_of_inertia

 

[chiralvandal]

thanks...
i'll try doing that now...

 

[chiralvandal]

are you supposed to derive the monent of inertia or are you allowed to look up the formula??

if ou allowed to look it up then go here
http://en.wikipedia.org/wiki/List_of_moments_of_inertia

i think i don't need to derive the formula for moment of inertia...
this page gives moment of inertia for a rod rotating perpendicular to its axis of rotation, but in this case its inclined... won't that change the situation?

 

[stunner5000pt]

i think i don't need to derive the formula for moment of inertia...
this page gives moment of inertia for a rod rotating perpendicular to its axis of rotation, but in this case its inclined... won't that change the situation?

is its axis of rotation perpendicular to the rod ?

 

[chiralvandal]

no it's not perpendicular...
the axis passes thro' the rod's midpoint and the rod rotates such that it forms a double cone...

 

[Mentz114]

See post #4

 

[chiralvandal]

the answer to the question is 84 joules...
that is given in the book but the working out isn't...

 

[chiralvandal]

In general, the MoI of a mass m rotating a distance r from its axis is m*r^2.

Work out the center of gravity for each arm, then use the perpendicular distance from the center of mass to the axis to get the MoI of each side.

i tried doing it using what you said...
Please see the attachment along with this post...

Any clues?

 

[chiralvandal]

some help please!

 

[chiralvandal]

you can't go wrong with a suggestion...