- #1

K.S

- 10

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**As a result of friction, the angular speed of a wheel changes with time according to**

dθ/dt = ω_o*e(-σt)

where ω_o and σ are constants. The angular speed changes from 3.50 rad/s at t=0 to 2.00 rad/s at t=9.30s.

(a) Use the information to determine σ and ω_o. Then determine

(b) the magnitude of the angular acceleration at t=3.00s,

(c) the number of revolutions the wheel makes in the first 2.50s, and

(d) the number of revolutions it makes before coming to rest.

dθ/dt = ω_o*e(-σt)

where ω_o and σ are constants. The angular speed changes from 3.50 rad/s at t=0 to 2.00 rad/s at t=9.30s.

(a) Use the information to determine σ and ω_o. Then determine

(b) the magnitude of the angular acceleration at t=3.00s,

(c) the number of revolutions the wheel makes in the first 2.50s, and

(d) the number of revolutions it makes before coming to rest.

Now, I can get part (a) to (c) - my answers are:

(a) ω_o = 3.50; σ=0.0602

(b) -0.176 rad/s^2

(c) 1.29 revs

However, I have in part (d) the expression

ω_o*e(-σt) = 0 ,

but I find there is no way I can get an answer from this expression, since ln0 is undefined.

Can anyone enlighten me please? Thanks in advance!

Source: Physics for Scientists and Engineers with modern physics, 8th edition, Serway and Jewett, page 318