# Homework Help: Question about mechanics

1. Apr 16, 2012

### winichris

2. Apr 16, 2012

### tiny-tim

welcome to pf!

hi winichris! welcome to pf!

show us what you've tried, and where you're stuck, and then we'll know how to help!

3. Apr 16, 2012

### winichris

Re: welcome to pf!

My teacher taught some very easy notes.
But he gave us this kind of so difficult problems.
I dont have ideas about that.

For Q1,
velocity of mass m = 2a x (g/a)^0.5

By conservation of momentum, m x 2a x (g/a)^0.5 = m x (velocity of ring)
velocity of ring will be = 2a x (g/a)^0.5

But I think this solution is wrong since by using conservation of energy:

0.5 x m x (velocity of mass)^2 = 0.5 x m x (velocity of ring)^2 + mgh

This will make h=0

So can you help me to think of this question?

4. Apr 16, 2012

### tiny-tim

you need to start by finding expressions for the momentum and the energy at a general speed v (of the ring) and angle θ

for horizontal momentum of the rod, you must use the velocity of the centre of mass of the rod

for kinetic energy of the rod, you must add the rotational kinetic energy (using moment of inertia about the centre of mass) to the "translational" kinetic energy of the centre of mass

start again!

5. Apr 19, 2012

### winichris

When the mass is at its highest point, its velocity and angular velocity are both zero?

6. Apr 19, 2012

### tiny-tim

when the rod is at its greatest angle, its angular velocity is obviously zero

but why would its ordinary velocity also be zero?

7. Apr 20, 2012

### winichris

http://imageshack.us/photo/my-images/823/phy.png/
When it is in the highest point, is the tangential velocity is zero? because v=rw, where w=0. (red blanket in the picture)

As the whole system is moving to right, so there should be a radial velocity of the mass ??(blue blanket in the picture)

But there is a question, there are 3 unknowns (angle theta, velocity of mass and velocity of ring) but there are only 2 equations.
So whether the radial velocity of the mass is equal to initial velocity of the mass?

Thanks a lot!

8. Apr 20, 2012

### tiny-tim

why are you using "radial" and "tangential"? there's no origin here (the ring is moving)
no, there are only 2 unknowns … position of ring, and angle of rod

9. Apr 20, 2012

### winichris

radial and tangential is for the rod (not the ring above).
Because when it is at highest point, w=0, can i conclude that tangential velocity=0?

Position of ring means velocity of ring?

10. Apr 20, 2012

### tiny-tim

yes of course
you can use either

11. Apr 20, 2012

### winichris

So with tangential velocity=0, the rod only consist of radial velocity.
Is the radial velocity (blue blanket in the last photo) = initial velocity of rod ( radius x angular velocity)

12. Apr 20, 2012

### tiny-tim

and what is y? and remember that there's no mass at the free end of the rod

13. Apr 20, 2012

### winichris

Let y be the radial velocity of the rod at highest point, x be the velocity of the ring when rod at highest point, v be initial velocity of the rod.
v=rw=2a(g/a)^0.5, right?
Will y and v be equal?

Momentum: mv = my cos(theta) + mx
Energy: 0.5mv^2 + 0.5Iw^2 = mg2a(1-cos theta) + 0.5mx^2 + 0.5my^2

14. Apr 20, 2012

### tiny-tim

the radial velocity is always 0
the rod doesn't have a velocity, it only has an angular velocity
(try using the X2 button just above the Reply box )

kinetic energy = 0.5mv2 for the ring + 0.5mv2 for the centre of mass of the rod + 0.5Iω2 for the rod

(and at the top of the swing, ω = 0)

15. Apr 20, 2012

### winichris

"when the rod is at its greatest angle, its angular velocity is obviously zero
but why would its ordinary velocity also be zero? "<-- you said that the rod should have zero velocity before.
Or maybe i misunderstand your meaning.
So the ordinary velocity of the rod should be zero at highest point?

16. Apr 20, 2012

### tiny-tim

no, i said the opposite ...

17. Apr 20, 2012

### winichris

Sorry i type wrongly.
You say the rod does not have an ordinary velocity here..

18. Apr 20, 2012

### winichris

Or maybe can you just tell me what will be the ordinary velocity of the rod when it is at highest point? thanks a lot, you are so helpful:)

19. Apr 20, 2012

### tiny-tim

the rod does not have an ordinary velocity, the rod has an angular velocity, and the centre of mass of the rod has an ordinary velocity

at its highest point, the angular velocity is 0, and therefore the velocity of the centre of mass of the rod is the same as the velocity of the ring

20. Apr 20, 2012