# Angular velocity and string tension

## Homework Statement

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.

## Homework 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

## 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......

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

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

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?

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

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

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...

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.

ok man thank for the help

gneill
Mentor
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.

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

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