Posted by **Kalen** on Wednesday, October 7, 2009 at 12:19pm.

We are learning about circular motion, uniform and non uniform. how do you find tension in a string, when the string is attached to a object with mass m and length r? What about if you are swinging it around in a horizontal circle and the string makes a angle theata with the horizontal?

- physics -
**MathMate**, Wednesday, October 7, 2009 at 12:41pm
If we ignore gravity, and calculate the tension in the string due solely to the circular motion, then

Tc=mrω²

where

Tc=tension due to circular motion

m=mass attached to the end of the string

r=radius

&omega=angular velocity, in radians / second

For a horizontal circular motion, the above value of Tc should be vectorially added to the weight, i.e.

Total Tension, T

= &radic(T²+(mg)^2)

The angle

tan^{-1}(mg/Tc)

is the angle with the horizontal.

For a vertical circular motion, Tc must be added to the vertical component of weight, -mg (positive upwards)

The vertical component can be obtained by -mg*sin(θ),

where θ=angle above horizontal, equals zero when mass is horizontal and going up.

Tension T

=Tc - mg*sin(θ)

- physics -
**bobpursley**, Wednesday, October 7, 2009 at 12:43pm
The only thing I would add to the above, is that the r in the formula for centripetal force is the radius of the horizonal circle, not the length of the string. if l is the length of the string, then r=lcosTheta. This makes Tc = mw^2 l cosTheta

- physics -
**MathMate**, Wednesday, October 7, 2009 at 12:46pm
Thank you Bob.

- physics -
**Kalen**, Wednesday, October 7, 2009 at 1:24pm
In the total tension, what does &radic mean?

Total Tension, T

= &radic(T²+(mg)^2)

The angle

tan-1(mg/Tc)

is the angle with the horizotal

- physics -
**MathMate**, Wednesday, October 7, 2009 at 1:29pm
Total Tension, T

= √(T²+(mg)^2)

The angle

tan-1(mg/Tc)

is the angle with the horizotal

√ is the equaivalent of square-root.

The formula is a typical application of Pythagoras theorem while adding the vertical and horizontal components of force. I could rewrite it as:

Total Tension, T

= sqrt(T²+(mg)^2)

The angle

tan^{-1}(mg/Tc)

is the angle with the horizotal

## Answer This Question

## Related Questions

- math - An object with mass m is attached to a string and the other end of the ...
- Physics - An object of mass m = 2.9 g and charge Q = +42 µC is attached to a ...
- Physics - An object of mass m= 4.8g and charge Q = 49uC is attached to a string ...
- physics - ball of mass m = 0.2 kg is attached to a (massless) string of length ...
- physics - A ball of mass m = 0.2 kg is attached to a (massless) string of length...
- physics - The system shown in the figure below consists of a mass M = 3.5-kg ...
- physics - A small sphere of charge q = +68 ƒÝC and mass m = 5.8 g is attached to...
- physics - A small sphere of charge q = +68 ƒÝC and mass m = 5.8 g is attached to...
- Physics - please check these answers for me When an object is moving with ...
- Physics - A ball of mass m = 0.2 kg is attached to a (massless) string of length...

More Related Questions