How Do You Calculate Angular Velocity and Centripetal Force for a Swinging Ball?

[Lyphta]

Homework Statement

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.

Homework Equations

ac=Rω
Fc=mac
v=Rπ

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?

 

[rock.freak667]

(a) v=rω
= (1.5)(2π/1.2 sec)
= 7.85 ft/sec

Check your units

(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

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?

 

[Doc Al]

Homework Equations

ac=Rω

I assume you mean:
$$a_c = \omega^2 r$$

(a) v=rω
= (1.5)(2π/1.2 sec)
= 7.85 ft/sec

Good. (Except for your units: Where did the feet come in?)

(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

OK, except: What are the units of force? (kg is a mass unit.) See note above regarding the formula.

(c) I have no clue at all what they want to solve... am I supposed to calculate the difference between a and b?

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

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