Rotational Motion of a thin rod about a pivot

[WWCY]

Homework Statement

A uniform thin rod of Length L and mass M is pivoted at one end is held horizontally and then released from rest. Assuming the pivot to be frictionless, find

a) Angular velocity of the rod when it reaches its vertical position
b) The force exerted by the pivot at this time
c) Now we want to swing the rod 270° clockwise so that it will reach a vertical position at the top of its swing. What initial angular velocity is needed for the rod to achieve that?

Homework Equations

Part a)
Parallel-axis theorem
Conservation of Energy

Part b)
∑F_cm = mω²r

Part c)
Conservation of Energy?

The Attempt at a Solution

I actually have no issues with parts A and B but only with C.

My initial concept for C was to use the principle of COE
U_{grav, 1} + K_{rotational, 1} = U_{grav, 2}
but this was wrong.

May I know what my concept for part c should be and why I was wrong in the first place?

P.s. Apologies if this post was not well done, it's my first post and feedback is appreciated. Thanks!

 

[conscience]

Part c)
Conservation of Ene
U_{grav, 1} + K_{rotational, 1} = U_{grav, 2}
but this was wrong.

Why do you think it is wrong ?

Please show your calculations and result you obtained .

 

[haruspex]

Having answered a, there is a very quick route to c.

 

[WWCY]

Damn, apologies everyone, my initial assumptions were right. I got confused because of some grading error. Sorry for taking up your time!

In any case it was:

U_grav1 + K _{rot 1} = U_grav2
1/2Iω² + mgL = mg(3/2)L
ω=(mgL/I)^1/2
where I = 1/3mL² with parallel axis theorem, which leads to:
ω = (3g/L)^1/2 rads/s

 

[haruspex]

Damn, apologies everyone, my initial assumptions were right. I got confused because of some grading error. Sorry for taking up your time!

In any case it was:

U_grav1 + K _{rot 1} = U_grav2
1/2Iω² + mgL = mg(3/2)L
ω=(mgL/I)^1/2
where I = 1/3mL² with parallel axis theorem, which leads to:
ω = (3g/L)^1/2 rads/s

Right... and do you see the connection with the answer to a?

 

[WWCY]

Right... and do you see the connection with the answer to a?

Apart from them being the same, I can't. Could you enlighten me?

 

[haruspex]

Apart from them being the same, I can't. Could you enlighten me?

In both cases the potential difference relates to a rotation from horizontal to vertical, and in both cases it is stationary at one end of the motion, so the speeds at the other end must be the same.

 

[WWCY]

In both cases the potential difference relates to a rotation from horizontal to vertical, and in both cases it is stationary at one end of the motion, so the speeds at the other end must be the same.

I never thought of it this way before, thank you for the insight.