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a particle moves with constant angular velocity in a circle.during the motion its 1)energy is conserved 2)momentum is conserved 3)energy and momentum both are conserved 4)none is conserved

a particle moves with constant angular velocity in a circle.during the motion its
1)energy is conserved
2)momentum is conserved
3)energy and momentum both are conserved
4)none is conserved

Grade:

4 Answers

Chetan Mandayam Nayakar
312 Points
9 years ago

Dear Nanda,

angular velocity and radius are constant. Therefore energy is conserved. even though speed is constant,direction is continuously changing. Therefore linear momentum is not conserved.

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CHETAN MANDAYAM NAYAKAR

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Nanda,

 

Since, angular velocity is constant.... we can only say it it's momentum = (mrw) is conserved.

 

It's KE will remain constant, but it's potential energy need not necessarily be a constant.

In case of particle moving in a vertical circle, the Total ebergy of the particle would not be conserved....

 

So Option (2), is the only definitve choice.

 

Best Regards,

Ashwin (IIT Madras).

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Nanda,

 

By momentum, it is meant the angular momentum is conserved....

 

Angular momentum, L = RXP { radius cross momentum}.... hence angular momentum is conserved, but not linear momentum, as its direction keeps changing.

 

Energy not necessary to be conserved, if rotating in Vertical Plane.

 

Regards,

Ashwin (IIT Madras).

Godfrey Classic Prince
633 Points
9 years ago

Dear Nanda RJ,

The energy is conserved !!! 

It is because the angular velocity & radius are constant !

 

Hope this helped you immensely...

All the very best & good luck to you ..

 

Regards,

AskIITians Expert,

Godfrey Classic Prince

IIT-M

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