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### Course: AP®︎/College Physics 1>Unit 5

Lesson 6: Conservation of angular momentum

# Conservation of angular momentum

How angular momentum is conserved within a system when there is no external torque.

## Want to join the conversation?

• Would gravity have an effect on the angular speed of the rock as it rotates around the planet?
• This is a really good question. I believe that gravity would not have an effect on the angular speed of the rock because gravity is a conservative force, and conservative forces do not affect the conservation of momentum or energy.
• I was solving this question

A child stands at the center of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value ? Assume that the turntable rotates without friction.

MY approach to this question is :-

let the movement of inertia of child be = I

initial I = I
final I = 2/5 * I

initial angular velocity = 40 rev / min = 4/3 π rad/s
final angular velocity = ?

since the energy is conserved
KE (initial) = KE (final)

(I ω^2) / 2 = (I ω^2) / 2
that's simplify to
ω (final) = 2/3 * sqrt(10) * π

but the correct answer according to my textbook is 100

my question is why my approach is wrong what knowledge is yet to fill in my head
• I calculated this using conservation of momentum and the fact that r final squared is just 2/5 of r initial squared, but got 10.47197551 rad/sec as an answer
(1 vote)
• what do you mean by external torque?
(1 vote)
• External torque is defined as an external source that supplies the force that causes rotation in a particular body.
• If there is no net torque, how does the skater speed up? Given the equation T = I*a, if torque is zero, angular acceleration should be zero. So how does the skater's angular velocity change? Or does the angular velocity of the center of mass not change?
(1 vote)
• For the "Conservation of angular momentum" practice problems, why do they substitute "mr^2" as the moment of inertia for a ball?
(1 vote)
• Why does L stay constant if the decrease is proportional to r^2 and w is only proportional to 1/r? Shouldn't L decrease if r gets smaller?
(1 vote)
• w is not proportional to 1/r. w is proportional to v/r, but v is a function of r.
(1 vote)
• How is there no external torque when force due to gravity is acting downwards and perpendicular to the radius of her spin?
(1 vote)
• Similar to linear collisions, are there cases of elastic and inelastic collisions involved for rotations?
I guess so as angular momentum isn't conserved when a rope spirals and binds around a pillar (system= rope+pillar)
and even for the skater right? As she is losing her angular momentum due to friction?
(1 vote)
• I remember reading that if the Angular momentum of a system has to be constant, it will be accompanied by a change in mechanical energy?
Consider: ball spiraling (binding) around a pole connected by a rope (frictionless surface + negligible air resistance), angular momentum is constant(say) but how is mechanical energy decreased?
(1 vote)
• at sal says omega that is analogus to angular speed but its commonly reffered as angular velocity, why?
(1 vote)