Question

A particle moves in a circular path with constant speed.
(i) On increasing speed, what happens to its angular momentum?
(ii) What will be the new angular momentum, if its kinetic energy is doubled and its angular frequency halved?

Answer 1

Answer:

Angular momentum, L=Iω...........(i)

Where, I is the moment of inertia

Kinetic energy,

K=

2

1

Iω

2

⟹K=

2

1

(I×ω)ω

⟹K=

2

1

Lω

(from eqn(i))

L=

ω

2K

.......ii)

Now, given angular frequency is halved, so, let ω

′

=

2

ω

And the kinetic energy is doubled, so, K

′

=2K

If L

′

is the new angular momentum, then using (ii) we can write,

L

′

=

ω

′

2K

′

⟹L

′

=

2

ω

2(2K)

⟹L

′

=4

ω

2K

⟹L

′

=4L

So, angular momentum becomes four times its original value.