I'm getting more and more confused.
The moment of intertia is the area under a curve, right? Then, of what curve? What kind of function is involved?
Is there a way to approach this integral as I approached the integral of the center of mass?
Thanks again for your help ;)
No, it does not. Here is the explanation the book gave the first time it expressed an infinite sum as an integral (when discussing center of mass):
"An ordinary object, such as a baseball bat, contains so many particles (atoms) that we can best treat it as a continuous distribution of matter...
Actually, I did find this wesbite. However, it is another example of what I said earlier: on the internet, functions are involved. When functions are involved, integration makes sense because the sum is the area under the curve.
However, here, I don't see a function. Thus, I don't understand why...
Well, I wouldn't have posted this question hadn't my preliminary Google research been unsuccessful.
On the internet, functions were always involved; but here, I don't see one, for the reasons I stated above.
And yes, I know that what is written in the textbook is right, but my question aims at...
Hello,
I am currently attempting to cover rotational motion using Halliday's Fundamentals of Physics.
I understand very well the concept of moment of inertia as defined as the sum Σmi*ri2.
However, the textbook argues that if there are too many particles, the moment of inertia can be defined as...
Homework Statement
Figure 8-36 shows an 8.00 kg stone at rest on a spring. The spring is compressed 10.0 cm by the stone. (a) What is the spring constant?
2. Relevant formula
Mechanical energy is conserved
The Attempt at a Solution
The decrease in gravitational potential energy that occurs...
I am indeed familiar with titled coordinate systems. But what you mention would rather look like this, wouldn't it?
http://img.sparknotes.com/content/testprep/bookimgs/sat2/physics/0014/tablewpulleyFBD.gif
This way of dealing with the problem doesn't seem very intuitive to me. I'm used to using...
Are you suggesting using F=ma for both blocks at once?
What do you mean by "the coordinate will bend at the pulley"? Is it mathematically consistent? I mean, I've never seen a coordinate system bending along the way.
Thanks for you help lightgrav ;)
The rope runs parallel to the incline.
I don't understand your next question, however. I mentioned the acceleration's components above; is that what you are talking about?
Thank you for your answer! :)
Oops, I did forget the signs indeed. Here's something better:
Block 1's acceleration's coordinates are:
(vector)a (-sinθ*g+T/m1, -cosθ*g +N/m1)
Block 2's acceleration's coordinates are:
(vector)a' (0,T/m2-g)
Since the rope is non-stretchable, ax and a'y have the...
Homework Statement
A block of mass m1= 3.70 kg on a frictionless plane inclined at angle θ=30.0° is connected by a cord over a massless, frictionless pulley to a second block of mass m2=2.30 kg. What are (a) the magnitude of the acceleration of each block, (b) the direction of the acceleration...