# Given initial angular velocity of wheel, find revolutions to rest

1. Jun 8, 2009

### pengwum

SOLVED Given initial angular velocity of wheel, find revolutions to rest

1. The problem statement, all variables and given/known data
As a result of friction, the angular speed of a
wheel changes with time according to
d $$\vartheta$$ / dt = 4.1e-.088335775t
where the initial angular velocity is 4.1 rad/s.
Find the number of revolutions it makes before coming to rest.

2. Relevant equations
d $$\vartheta$$ / dt = 4.1 rad/s-.088335775t

3. The attempt at a solution
To find the time needed for the wheel to rest, I set the left side of the equation to 0, but to find t, I had to find the natural log of both sides. However, ln of 0 does not exist...so now I am at a loss. Any help would be appreciated...thanks!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

Last edited: Jun 8, 2009
2. Jun 8, 2009

### rl.bhat

First of find the angular acceleration by taking he derivation of angular velocity.
α =kω, where k = -0.08833577.
Then use the equation θ =Intg [( ω^2 - ωο^2)/2α]*dω between the limits ωο to 0, find the total angular displacement. From that you can find the number of rotations.