Angular Deceleration of a Bicycle Wheel

[bmoore509]

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 measures the height reached by drops moving vertically. A drop that breaks loose from the tire on one turn rises 49.8 cm above the tangent point. A drop that breaks loose on the next turn rises 46.8 cm above the tangent point (the angular speed of the wheel is decreasing).
Find the angular deceleration of the wheel. The acceleration of gravity is 9.8 m/s2 . Assume the angular deceleration is constant.
Answer in units of rad/s2.

Homework Equations

.5mv_i^2=mgh₁
w=v/r
w_f^2=w_i^2+2(alpha)(thetafinal-thetainitial)

The Attempt at a Solution

r=0.4 m
h₁= 0.498 m
h₂=0.468 m
Change of theta=2pi (I'm a little confused on this. Would it be 2pi or 4pi?)


I got v₁=3.124227905 m/s
v₂=3.028663071 m/s
w₁ = 7.81059763
w₂ = 7.571657678

w₂^2=w₁^2+2(alpha)(changetheta)
7.57165678^2=7.810569763^2+2(2pi)a
a=-0.29244721 rad/s^2

I don't know where I went wrong but that answer isn't correct.

 

[rl.bhat]

Your angular displacement is correct. But angular velocity is wrong. You have not used the radius of the wheel.
v = rω. so angular velocity = v/r.
Now proceed.

 

[bmoore509]

I don't understand how that's not what I did.

3.124227905/0.4=7.81059763

 

[rl.bhat]

I don't understand how that's not what I did.

3.124227905/0.4=7.81059763

You are right. Your answer appears to be correct.

 

[bmoore509]

It's not, though because it's an online homework and the online homework says its wrong.

 

[rl.bhat]

It's not, though because it's an online homework and the online homework says its wrong.

They have asked the angular deceleration. So change the sign and submit.