Rotational Motion of a Hanging Mass

[interxavier]

Homework Statement

Consider a ball of mass m on the end of a string of length l. It hangs from a frictionless pivot. The ball is pulled out so that the string makes an angle thetai with the vertical and is then released.
a. Find w (angular velocity) as a function of the angle the strings makes with the vertical. (Hint: Use conservation of energy.)
b. Find the angular momentum of the ball using |L| = ml^2w
c. Show that t = dL/dt by differentiating L and finding t from its definition.

Homework Equations

U1 + K1 = U2 + K2
V = rw

The Attempt at a Solution

for a:

The answer, according to the book, is w = sqrt(2g/l*(cos(theta) - cos(thetai)))

I used the conservation of energy and got w = sqrt(2g/l*(1 - cos(thetai))). I'm lost.. I don't know where the book got cos(theta)

 

[rock.freak667]

at an angle θ_i, find the energy at that point.

Now this energy is converted into gravitational pe and ke at an angle θ. Find this energy here.


Equate the two.