# Tangential Speed

1. May 12, 2008

### grouchy

[SOLVED] Tangential Speed

A 4k ball is attached to a vertical rod with a cord 1.6 m long. As the ball rotates around the vertical rod in a circle of radius R = 0.8 m, what is the tangential speed of the ball?

Any help is appreciated.

2. May 12, 2008

### sirzerp

You need more information. What was the speed when the radius was 1.6m?

You need some kind of time information.

3. May 12, 2008

### grouchy

Oh, forgot to add that the angle that the string makes with the rod is 30 degrees

4. May 12, 2008

### Jason03

Picture the following force diagram. The string is the hypotenuse of a right triangle. The vertical side of the right triangle is equal to the weight of the ball $$mg$$ while the horizontal side is equal to the centripetal force $$F_{c}$$ acting on the ball [keeping the ball moving in a horizontal circle]. The angle between the vertical side of the triangle and the hypotenuse is 30 degrees as given. The forces are vectors and are therefore related through the tangent function:
tan30=Fc/mg from which we can find the centripetal force
Fc=mg*tan30=4*9.8*tan30
Since centripetal force is equal to Fc=m*v^2/R all you need to know now is the radius of the circular path which is given....
Finally, solve for v: v=sqrt[Fc*R/m]

$$F_{c} = (mg)Tan\theta$$

$$V = \sqrt\frac{F_{c}(r)}{m}$$

Last edited: May 12, 2008
5. May 12, 2008

### grouchy

Ok, that makes sense. Thx for your help.