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Conical pendulum
By Raja Manikam Vittal (P1156) on Tuesday, August 31, 1999 - 06:45 am:

Could you please explain why there must be a force acting on a particle which is moving in a circular path. Could you please give an expression for its magnitude?
Question 1:
A conical pendulum consists of a small massive bob hung from a light string of length 1m and rotating in a horizontal circle of radius 30cm.With the helop of a digram please indicate what forces are acting on the bob?Deduce the speed of rotation in revolutions per minute.

Question 2:
Is there difference in speed for a ball moving horizontally and vertically?

Ouestion 3:
Could you please draw me a diagram of a pendulum"s moving horizontally when it suddenly the string joint to it snaps?

I certainly appreciate your kind asistance in helping solve these questions.

By Graham Lee (P1021) on Friday, September 3, 1999 - 06:51 pm:

I'm not one of the dedicated team etc., but I'll give this a go.
If you have done Newton's laws, the 1st law states that "a body will remain at rest or in motion at a constant velocity unless an external force is acting upon it". Now what this means is that if you left a particle alone, it would go in a straight line. Consider a stone on a string. If you whirl it around your head, it will follow a circular path. If you let go of the string, it will fly off tangentially.
The force, in this case the tension in the string, is called Centripetal Force, and it always acts toward the centre of the circle.
An expression for the force is F=mrw², where w is Omega, the angular velocity (in rad/s).
acceln=rw²
tangential velocity=rw
period=2pi/w.
With these you should be able to get somewhere with the other q's.

Graham.

By Chris Jefferson (Caj30) on Sunday, September 12, 1999 - 10:46 pm:

If an object is going in circular motion, then there is a force pointing toward the center of the circle it is travelling in of

F=mv2/r or F=mrw2

Where v=rw

and v is the speed of the particle in m/s, and w is the angular speed in rad/s

The reason a particle doesn't go in a circle without a force is... erm.... it doesn't!

You will be told that Newton's laws say so, they say that a particle will, with no external force either stay stationary or more in a straight line at constant speed. The reason we accept this law is because no-one has ever seen any particles break it...

Now, when you say horizontally and vertically, I assume you mean looking down at the pendulum from above. Your inital thought should be that as the pendulum is the same all the way around one rotation, there shouldn't be any difference, and you'd be right!

Anyway, on to the next question... It will probably be easiest to give a picture now...

Picture of the pendulum

I hope you can see that, or else this could get complicated..

Now, the pendulum is moving into (or out of) the page at the clip, I hope you can imagine it. Now the easiest way to do this question is by 'resolving' forces in some direction..

Now first, look in the direction of gravity. In this direction there is all of gravity (mg), a component of the tension, which you can work out by digging out some trigonometry (The hypotenuse is 1, the opposite side is 0.3 so sin a=0.3 and T(cos a)-mg=0, so we've worked out T
Now look perpendicular to gravity, and we have T(sin a)= mrv2, so we can work out v!

I'm skipping over that bit quite quickly, I assume you have done resolving of forces. If not, sorry! Come back and tell me.

When the string snaps, the bob will start moving in a straight line horizontally, well... gravity will start dragging it down as well, but that just makes things difficult. The particle will basically act like it has been fired out of a stationary cannon in the same place where the string snapped.

I hope that helps, write back if you need anything explaining

Chris Jefferson