What is the Angular Deceleration of a Bicycle Wheel?

[cdubsean]

Homework Statement

A bicycle is turned upside down while its
owner repairs a flat tire. A friend spins the
other wheel of radius 0.4 m and observes that
drops of water fly off tangentially. She mea-
sures the height reached by drops moving ver-
tically. A drop that breaks loose from the tire
on one turn rises 36.3 cm above the tangent
point. A drop that breaks loose on the next
turn rises 31.6 cm above the tangent point
(the angular speed of the wheel is decreas-
ing).

Find the angular deceleration of the wheel.
The acceleration of gravity is 9.8 m/s2 . As-
sume the angular deceleration is constant.
Answer in units of rad/s2.

Homework Equations

Max height = (Vi^2)/2g
2pi(r)
Angular Velocity

The Attempt at a Solution

Given what I know I converted units
36.3 cm to .363m
31.6 cm to .316m

Then used max height formula to determine the Vi

Vi1 = 2.6674 m/s
Vi2 = 2.4887 m/s

and with this I can find the time buy using the circumference and the velocities to determine the times.

T1= .9422s for one complete cycle
T2= 1.0099s for one complete cycle

And with this I need to use angular acceleration formula to get this, but here is where I am lost and fell like I am going in wrong direction. Can I get some guidance into what I should do next. I know that I might have to use this to find tangent line which between these two to find acceleration...in this cause deceleration. But I am lost.

 

[Doc Al]

and with this I can find the time buy using the circumference and the velocities to determine the times.

T1= .9422s for one complete cycle
T2= 1.0099s for one complete cycle

Instead of this, which assumes constant speed over the course of each cycle, trying using a different kinematic formula that gives you the acceleration directly.

How do you convert tangential quantities (distance, speed, acceleration) to angular quantites?