Angular velocity of a conical pendulum in rpm

[kerbyjonsonjr]

Homework Statement

A conical pendulum is formed by attaching a 0.900 kg ball to a 1.00 m long string, then allowing the mass to move in a horizontal circle of radius 20.0 cm . What is the ball's angular velocity, in rpm?

Homework Equations

v=$$\sqrt{}L*g*sin(\vartheta)*tan(\vartheta)$$
w=v/r

The Attempt at a Solution

Since the radius is .2 m and the length of the string is 1m I used cos($$\vartheta)$$ and found $$\vartheta$$ to be 78.46 degrees. Then I used that equation for tangential velocity so I had v=$$\sqrt{}1*9.81*sin(78.46)*tan(78.46)$$ and got v=6.86 m/s so then I used w=v/r and got w=34.3 rad/sec which I then converted to rpm by multiplying 34.3 by 60 seconds times 1 rev/2$$\pi$$ and got 327.5 rpm and that is wrong. I don't know where I went wrong. I greatly appreciate any help.

 

[hage567]

Homework Statement

A conical pendulum is formed by attaching a 0.900 kg ball to a 1.00 m long string, then allowing the mass to move in a horizontal circle of radius 20.0 cm . What is the ball's angular velocity, in rpm?

Homework Equations

v=$$\sqrt{}L*g*sin(\vartheta)*tan(\vartheta)$$
w=v/r

The Attempt at a Solution

Since the radius is .2 m and the length of the string is 1m I used cos($$\vartheta)$$ and found $$\vartheta$$ to be 78.46 degrees. Then I used that equation for tangential velocity so I had v=$$\sqrt{}1*9.81*sin(78.46)*tan(78.46)$$ and got v=6.86 m/s so then I used w=v/r and got w=34.3 rad/sec which I then converted to rpm by multiplying 34.3 by 60 seconds times 1 rev/2$$\pi$$ and got 327.5 rpm and that is wrong. I don't know where I went wrong. I greatly appreciate any help.

I don't think you have the right angle. Double check how you got that.