As a result of friction, the angular speed of a wheel changes with time according to
d(theta)/dt = w0 e^-(aplpha*t)
where w0 and alpha are constants. The angular speed changes from an initial angular speed of 4.87 rad/s to 4.27 rad/s in 33.93s.
A) Determine the magnitude of the angular acceleration after 2.46s. answer in rad/s^2
B) How many revolutions does the wheel make after 2.59 s? answer in rev
C) find the number of revolutions it makes before coming to rest, answer in rev.

any help would be appreciated, thank you in advance

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  1. angular speed=dTheta/dt

    angular acceleration=d"theta/dt"
    = -alpha*wo e^{-alpha*t)

    now given: speed(t=0)=wo=4.87
    speed(t=33.93)=4.87e^(-alpha*33.93) solve for alpha
    take the ln of each side,
    ln (4.27)=ln(4.87)-alpha*33.93
    solve for alpha

    for b, integrate dTheta/dt from t=0 to t=2.57

    for c. rest means dTheta/dt is zero, so solve for t when dTheta/dt=0, notice that it NEVER gets to rest, so tf=infinity.

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