You have tied a rock to a piece of string and are spinning it around your head.

Question

You have tied a rock to a piece of string and are spinning it around your head. Eventually, you will let it go and it will fly off and break something valuable but for now let's discuss the rock as it spins on the string. The rock has a mass of 1 kg. Its circular path has a radius of .5 m and it makes two revolutions per second. Find the tension of the string.

The next step was for me to analyze the circular motion:

r = .5, Vt = 6.29, Ar= 79 ---> are those right?

The next step was for me to calculate the forces:

The next step is to  solve for an expression for the angle the string will make with the horizontal. Not sure how to do this :(

Explanation / Answer

angular speed of rock, w = 2 rev/s

= 2*2*pi rad/s

= 12.57 rad/s

radial acceleration, a_rad = r*w^2

= 0.5*12.57^2

= 78.96 m/s^2

Now use Newton's second law, Fnet = m*a_rad

Tx = m*a_rad

= 1*78.96

= 78.96 N

Ty = m*g

= 1*9.8

= 9.8 N

so, tension in the rope, T = sqrt(Tx^2 + Ty^2)

= sqrt(9.8^2 + 78.96^2)

= 79.6 <<<<<<<----------Answer

angle made with vertical by string, theta = tan^-1(Tx/Ty)

= tan^-1(78.96/9.8)

= 82.9 degrees <<<<<<<---------Answer

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