physics
posted by Kalen .
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?

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) 
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

Thank you Bob.

In the total tension, what does &radic mean?
Total Tension, T
= &radic(T²+(mg)^2)
The angle
tan1(mg/Tc)
is the angle with the horizotal 
Total Tension, T
= √(T²+(mg)^2)
The angle
tan1(mg/Tc)
is the angle with the horizotal
√ is the equaivalent of squareroot.
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
Respond to this Question
Similar Questions

Physics
An object of mass m= 4.8g and charge Q = 49uC is attached to a string and placed in a uniform electric field that is inclined at an angle of 30.0 with the horizontal (see the figure). The object is in static equilibrium when the string … 
physics
A ball of mass m = 0.2 kg is attached to a (massless) string of length L = 3 m and is undergoing circular motion in the horizontal plane, as shown in the figure. What should the speed of the mass be for θ to be 46°? 
physics
ball of mass m = 0.2 kg is attached to a (massless) string of length L = 3 m and is undergoing circular motion in the horizontal plane, as shown in the figure. What should the speed of the mass be for θ to be 46°? 
math
An object with mass m is attached to a string and the other end of the string is attached to a peg at the center of a level table. The object is set into uniform circular motion around the peg. The radius of the motion remains constant … 
physics
The system shown in the figure below consists of a mass M = 3.5kg block resting on a frictionless horizontal ledge. This block is attached to a string that passes over a pulley, and the other end of the string is attached to a hanging … 
Physics
An object of mass m = 2.9 g and charge Q = +42 µC is attached to a string and placed in a uniform electric field that is inclined at an angle of 30.0° with the horizontal. The object is in static equilibrium when the string is horizontal. … 
physics
You create a centripetal force apparatus consisting of a mass m attached to the end of a string and spun in a uniform circular path of radius R, where R = 65.5 cm. The mass is spun in a uniform circular path for 60.0 seconds, during … 
Physics
A mass is tied to a 1 m string. The string is attached to a point on a horizontal frictionless surface and the mass is set into circular motion. The string will break if tension becomes larger than 10 N. The maximum kinetic energy … 
Physics  Tension Question
A uniform bar of mass 12 kg and length 1.4 m is held by a hinge on a vertical wall. A string is attached to the end so that the bar is in mechanical equilibrium. The angle between the bar and the string is 25o. Find the tension in … 
Physics: HELP PLS
The speed of a wave in a string is given by v = Ö(FT/m), where FT is the tension in the string and m = mass / length of the string. A 2.00 m long string has a mass of 15.5 g. A 93 g mass is attached to the string and hung over a pulley. …