How Many Revolutions Does the Wheel Make in 2.33 Seconds?

[jj8890]

Homework Statement

As a result of friction, the angular speed of a wheel changes with time according to
d θ/d t = ω_0 e^(−σ t) ,
where ω0 and σ are constants.
initial angular speed = 5.45 rad/s
σ =.23913
Determine the number of revolutions the wheel makes after 2.33 s .
Answer in units of rev.

The Attempt at a Solution

I know I have to take the integral which is:
θ = - w_0/(σ *e^(-σ *t))
My numbers are initial velocity= 5.45 rad/sec, sigma= .023913, and time=2.33 seconds. so when I solved I got -13.0589 radians and divided it by 2pi to get revolutions, which gave me -2.07839. I thought the answer would be 2.07839 because revolutions can't be negative but it is not right, should i use the negative or am i doing something wrong?

 

[tiny-tim]

Determine the number of revolutions the wheel makes after 2.33 s .
Answer in units of rev.

{snip} … so when I solved I got -13.0589 radians and divided it by 2pi to get revolutions, which gave me -2.07839. I thought the answer would be 2.07839 because revolutions can't be negative but it is not right, should i use the negative or am i doing something wrong?

Hi jj!

I'm with you on this: the question is badly worded.

The wheel makes 2.07839 revolutions clockwise!

However, that's clearly not the answer they want - if this is a computer thing where you're only allowed to put in a number, then you must put in the number they want - this isn't a constitutional rights case!

But if you're allowed a full answer, write something like "-2.07839 revolutions in the direction of increasing θ (2.07839 revolutions in the direction of decreasing θ)" - with the answer they want first.