# Angular velocity and string tension

1. Jul 21, 2011

### druuuuuuuunnk

1. The problem statement, all variables and given/known data

A ball of mass 0.13 kg, is whirled round in a horizontal circle, on the end of a
string of length 0.60m, and completes 5 revolutions per second.
Calculate:

(a) the angular velocity of the ball;
(b) the speed of the ball;
(c) the tension of the string.

2. Relevant equations

(a) Angular velocity = (2) x (Pi) x (Frequency of revolutions)
(b) Speed of ball = (radius) x (angular velocity)
(c) tension in string = (mass) x (initial speed*2)
........................................divided by 2

* = To the power of

3. The attempt at a solution

(a) Angular velocity = 31.4 rad/s
(b) Speed of ball = 18.84 m/s
(c) Tension in string = ???

im confused about part (c) the question does not give an initial speed, so do i use the velocity i have got from part (b) is it not the same thing or would it be wrong to do that?

any help is appreciated......

2. Jul 21, 2011

### Pi-Bond

The velocity in your tension formula is the linear velocity at which uniform circular motion is being executed.

Last edited: Jul 21, 2011
3. Jul 21, 2011

### druuuuuuuunnk

im new to this physics thing! i came from a art course last year so if you could say that in terms i would understand that would be awesome. Are you saying that i've got the wrong formula?

4. Jul 21, 2011

### Pi-Bond

No, your formula is alright. The velocity you got in (b) is the linear velocity (you should remember this).

5. Jul 21, 2011

### druuuuuuuunnk

Im not gonna lie, im alot more confussed now, than i was before. i think you over-estimated my physic knowledge haha

so how can part (b) be linear velocity? isn't linear velocity = distance /over/ time

and how do i find the tension of the string...

6. Jul 21, 2011

### Pi-Bond

Yes, what you said about linear velocity is right. In case of the circle, the distance would be along the circumference of the circle. And in this type of motion, you can relate the angular velocity and linear velocity by the formula you used in (b).

The force required to keep an object in circular motion is given by

$\frac{mv^{2}}{2}$

In this case the force is the tension force of the string.

7. Jul 21, 2011

### druuuuuuuunnk

ok man thank for the help

8. Jul 21, 2011

### Staff: Mentor

Make that:
$$\frac{m v^2}{r}$$
(No doubt the 2 was a typo)

9. Jul 22, 2011

### Pi-Bond

Right, that was a typo, I just copied from OP's post without thinking :/