# Angular Velocity of a ball

1. Jan 14, 2008

### Lyphta

1. The problem statement, all variables and given/known data
Imagine that you swing about your head a .250 kg ball attached to the end of a string. The ball moves at a constant speed in a horizontal circle with a radius of 1.50 m. If it takes 1.20 seconds for the ball the make one revolution, (a)what is the ball's tangential speed? (b)What centripetal force are you imparting to the ball via the string? (c)Can the string be exactly horizontal.

2. Relevant equations
ac=Rω
Fc=mac
v=Rπ

3. The attempt at a solution
(a) v=rω
= (1.5)(2π/1.2 sec)
= 7.85 ft/sec
(b) ac=Rω
= 1.5 [(1 rev/1.2 seconds)(2π/ 1 rev)]^2
= 41.12 ft/sec^2
Fc=mac
= (.25 kg)(41.12 ft/sec^2)
= 10.28 kg
(c) I have no clue at all what they want to solve... am I supposed to calculate the difference between a and b?

2. Jan 14, 2008

### rock.freak667

Units again...Unit of Force is the Newton(N)...units of acceleration ms^-2

For part (c) if the string is perfectly horizontal, what forces are acting on the ball and string?

3. Jan 14, 2008

### Staff: Mentor

I assume you mean:
$$a_c = \omega^2 r$$
Good. (Except for your units: Where did the feet come in?)
OK, except: What are the units of force? (kg is a mass unit.) See note above regarding the formula.

Study the forces acting on the rock. What role does the string play?

[I see that rock.freak667 beat me to it! ;-)]