Calculating Rotational Kinetic Energy of a Falling Ball-Rod System

[Momentum09]

Homework Statement

A cylindrical rod 36.4 cm long has mass 0.655kg and radius 1.1cm. A 18.5kg ball of diameter 11.4cm is attached to one end. The arrangement is originally vertical with the ball at the top and is free to pivot about the other end. After the ball-rod system falls a quarter turn, what is its rotational kinetic energy?

Homework Equations

KEr = 1/2 Iw^2.
mgh = 1/2Iw^2 + 1/2 mv^2.

The Attempt at a Solution

I found the moment of inertia of the ball-rod system, but then I don't know what to do next.

 

[Doc Al]

How are they defining "rotational KE"? Do they mean rotational KE about the center of mass? (The object can be considered to be in pure rotation about the end point, and thus all its KE is rotational KE about that point.)

If they mean rotation KE about the center of mass, then use [itex]v = \omega r_{cm}[/itex] to relate rotational and translational speeds.

 

[Dick]

During the quarter turn rotation what is the vertical displacement of the center of mass? Hence what can you say about the change in gravitational potential energy of the system? Where does that energy go? Looks pretty clear to me that they mean you to consider rotational energy about the pivot point, so yes, consider all motion rotational.

 

[Doc Al]

Looks pretty clear to me that they mean you to consider rotational energy about the pivot point, so yes, consider all motion rotational.

If that's the case, then no need to find the moment of inertia. (To me it's still a bit ambiguous.)

 

[Dick]

If that's the case, then no need to find the moment of inertia. (To me it's still a bit ambiguous.)

Good point. Please ignore things that "are pretty clear to me" without foundation.

 

[Momentum09]

Thank you so much! I got it.

 

[Momentum09]

So if I were to find the angular speed of the system at that point, would I just do
Rotational Kinetic energy = 1/2 Iw^2, where I = 1/3ML^2 + 2/5MR^2 + (L+R)^2?

 

[Dick]

Thank you so much! I got it.

So the rotational axis they are referring to IS through the pivot point?? No translational KE after all?

 

[Momentum09]

yes just rotational KE

 

[Dick]

yes just rotational KE

Then, yes, just use moment of inertia to solve for angular velocity. I notice you've included the R of the sphere to the parallel axis part for the sphere. So you have decided that the ball is glued on to the end of the rod? (BTW you only have one M symbol in your moment expression and none at all on the (L+R)^2 part. Just typos, right?).

 

[Momentum09]

lol yeah :)