Torque graph; finding angular velocity

[animanga008]

An object whose moment of inertia is 4.10 kg/m^2 experiences the torque shown in the graph attached.

What is the object's angular velocity at 2.70 s? Assume it starts from rest.

My main problem i think is how to read the graph. How should i interpret the graph?

What i would do first is find the angular acceleration by using...

aa = angular acceleration
t = torque
I = moment of inertia

aa= t/I

I would find the aa for three parts, the part where it is accelerating positively, when it is not increasing, and then when it decreases.

I would then use the aa for the equation while putting in the velocity...

w = angular velocity
T = time

w(f) = w(i) + aaT

 

[Nadialy]

i wish they would reply, i would like help with this also.

 

[rohanprabhu]

Well.. you have the Torque as a function of time. Break it up into 3 different functions, one for each of the time interval. At t=2, you can take it to be a part of either of the time interval, just make sure you include it in ONE and ONLY ONE of them.

Once you have $\tau (t)$, divide it by $I$ to get $$\alpha (t) = \frac{1}{I} \tau (t)$$.

Then integrate it w.r.t to get the angular velocity in each of these intervals using proper limits. This might help you:

$$\Delta \omega = \int_{t_1}^{t_2} \alpha (t) dt$$

Here, $\Delta$ is used to denote that I'm computing the change in angular velocity since the given acceleration was applied. If the initial angular velocity was 0, you can take $\Delta \omega = \omega$. Once you have done that, you'll need to addup the angular velocities [or their differences rather] attained in each time interval. Do note that, no net torque doesn't mean zero angular velocity, it just means a zero change in angular velocity. Reply if you have any problems with this.

 

[tiny-tim]

Welcome to PF!

My main problem i think is how to read the graph. How should i interpret the graph?

Hi animanga008! Welcome to PF!

(btw, your original post was at 4am here in London, and just before midnight in New York … if you want a quick answer, you probably need to start a bit earlier!)

The torque is only in two parts.

(1) The torque increases steadily from t = 0 to 1, according to the formula tau = 2t (so, for example, at t = 1/4, tau = 1/2)

(2) The torque is then steady for one second.

After that, it disappears suddenly (in no time at all)!

 

[appelle moi]

Can anyone tell me why does the car engine have maximum power of e.g. 120 horsepower at 4200 revs per minute, and maximum torque of 250 Nm from 1400-2600 revs per minute?

The car seems to have the best acceleration in the range of the greatest torque (1400-2600 revs per minute), but not at maximum power (4200 revs per minute). What is the catch?

 

[rohanprabhu]

Can anyone tell me why does the car engine have maximum power of e.g. 120 horsepower at 4200 revs per minute, and maximum torque of 250 Nm from 1400-2600 revs per minute?

The car seems to have the best acceleration in the range of the greatest torque (1400-2600 revs per minute), but not at maximum power (4200 revs per minute). What is the catch?

Given the date of the post, I would suggest you start a new thread with your question. Please do not bump topics so old when the post content is not explicitly related to that of the op. Thank you.