# Uniform vertical circular motion

1. Dec 28, 2009

### twinklestar10

1. The problem statement, all variables and given/known data
An object of mass m is attached to a light rod of length r which is driven by a motor at a steady rate. The object performs uniform vertical circular motion.
Centripetal force is provided by tension and weight.
Draw the net force acting on the mass when the mass is at a height of r from the bottom of the circular path.

2. Relevant equations
Net force = T + mg

3. The attempt at a solution
so I draw the net force which is pointing inwards, but at the same time, a bit downwards rather than solely towards the centre of the circular path

but isn't the net force of a uniform circular motion pointing towards the centre of the circular path all the time?

Can anyone help me to draw the free body diagram of the mass and explain it to me?

2. Dec 28, 2009

### sylas

Why would it not point direct to the center of the path?

3. Dec 28, 2009

### Redbelly98

Staff Emeritus
Welcome to PF

Since it is a rod, not a rope or string, the force it exerts is not simply tension along the rod's length.

p.s. Hello Sylas.

4. Dec 29, 2009

### twinklestar10

but there is no tangential acceleration as the speed is uniform,
so only centripetal acceleration exists...
that means total acceleration is actually centripetal acceleration,
by F=ma, net force should be centripetal too, isn't it?
how come the correct answer isn't like that?

5. Dec 29, 2009

### Staff: Mentor

Sounds good to me.
What do they claim is the correct answer?

6. Dec 30, 2009

### twinklestar10

they claim that...
in the case when the mass is at a height of r
the net force shouldn't be 100% centripetal, but it is at a small angle to the horizontal, say pointing towards 8 o'clock
because there are 2 forces acting on it: weight & tension
I understand this, and from this I can deduce the vector sum of forces which is really not totally centripetal,
but, the speed of the ball is uniform, which means there shouldn't be tangential acceleration, and from this, I can deduce that the total force should only be centripetal...
Did I make any mistakes?

7. Dec 30, 2009

### Staff: Mentor

You are correct--the book is wrong. Just because two forces act doesn't mean that the net force is not completely centripetal.

8. Dec 30, 2009

### twinklestar10

But it seems not to agree with the free body diagram --- tension + weight,
how can I get the vector sum as a centripetal one?

9. Dec 30, 2009

### Staff: Mentor

As Redbelly98 hinted above, the force exerted by the rod is not simply a tension--it can exert a sideways force as well. (Otherwise it couldn't produce uniform vertical circular motion.)

10. Dec 30, 2009

### twinklestar10

actually i have an idea...
do you think that the motor would also provide a force directing up (static friction between the rod and the mass?!) in order to move the mass?
that means there are 3 forces,
tension, weight & this upward force
then i can conclude that the vector sum can be 100% centripetal because this upward force balances the weight, what's left is only the tension.
What do you think?

11. Dec 30, 2009

### twinklestar10

Anyway, so I now understand the problem I encountered before,
the key is that I didn't realize there was a third force besides tension, provided by the rod.
and that exactly can cancel the weight when the mass is at a height of r,
this leads to the centripetal net force at that moment.

Thanks a lot to both mentors!

12. Dec 30, 2009

### tiny-tim

Hi twinklestar10!

Forget tension …

a rod doesn't have longitudinal tension.

(If this was a string, the tension would be along the string, but there would be no way to make the motion uniform )

13. Dec 30, 2009

### Redbelly98

Staff Emeritus
[STRIKE]Twinklestar, yes, there is an additional upwards force. It is the sideways force (not tension) that is exerted by the rod on the object. The motor exerts this force on the rod, which in turn exerts the force on the object.[/STRIKE]

EDIT:
Ah, nevermind, you've got it

You're welcome!