Angular velocity (check it out n tell me what u guys think)

[phy_bits]

angular velocity...(check it out n tell me what u guys think)

hello ppl...

consider this problem...

u could refer 2 resnick n halliday 5th edition, the 3rd author is krane. chapter 10, problem no. 8.

theres a disc that's rotating about a horizontal axis with angular velocity 'w'. a small mass 'm' just chips off n flies vertically upwards as the disc is rotationg, what is the final angular velocity of the disc.


now when the chip flies off, it has a linear vel= r.w
is it correct to assume it also has an instantaneous angular velocity= w ?

also refer problem 2 in the same chapter, it says 2 particles (mass 'm' each) r moving in opp directions with speed 'v' along parallel lines sep. by a dist. 'd' find the total angular momentum of system abt any origin.

the second problem requires us to find angular momentum of particles which r moving in st lines. r v req. to make a hypothetical assumption n find the ans. or do the actually have angular velocity.

on similar lines. if we assume the mass 'm' that chips off to have an angular velocity then the result obtained is that the disc continues to rotate with the same angular velocity. does that mean everytime we remove a portion of mass frm the disc, it continues to rotate with same ang. vel. 'w'?

please just answer the question ...do all bodies moving with linear velocities have ang. vel w.r.t a fixed point?

waiting 4 an answer...


bye

 

[whozum]

For the first problem, you'll want to note that angular momentum is conserved. If the piece flew off, you have a little change in the moment of inertia, which will result in a change in angular velocity.

Try showing some effort on the problem, #2 is hard to decipher.

 

[quicknote]

Hi there,

Thank you for your question. I would like to provide you with a response to the concept of angular velocity.

Angular velocity is a measure of how fast an object is rotating around a fixed point, usually measured in radians per second. It is different from linear velocity, which measures how fast an object is moving in a straight line.

In the first problem you mentioned, the chip flying off the rotating disc does indeed have an angular velocity. This is because it is rotating around the center of the disc, and its distance from the center (r) and the disc's angular velocity (w) determine its angular velocity (r.w). This is true for all objects that are rotating around a fixed point.

In the second problem, the particles moving in opposite directions also have angular momentum because they are moving in a curved path around a fixed point (the origin). The total angular momentum of the system can be calculated by adding the individual angular momentums of each particle.

In the case of the disc, every time a portion of mass is removed, the disc will continue to rotate with the same angular velocity (assuming no external forces act on it). This is because of the principle of conservation of angular momentum, which states that the total angular momentum of a system remains constant unless acted upon by an external torque.

To answer your final question, not all bodies moving with linear velocities have angular velocity with respect to a fixed point. Only objects that are moving in a curved path around a fixed point have angular velocity. Objects moving in a straight line do not have angular velocity.

I hope this explanation helps. Please let me know if you have any further questions.

Best,