Given initial angular velocity of wheel, find revolutions to rest

[pengwum]

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

Homework Statement

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.

Homework Equations

d $$\vartheta$$ / dt = 4.1 rad/s^-.088335775t

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!

 

[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.

 

[nlightner]

To find the time needed for the wheel to come to rest, we can set the angular velocity to 0 and solve for t. This gives us t = 46.5 seconds. We can then use this time to find the number of revolutions by multiplying it by the initial angular velocity (4.1 rad/s) and dividing by 2π, since each revolution is equal to 2π radians. This gives us approximately 30 revolutions before the wheel comes to rest.