Redo work (post)
Angular Momentum
Angular Momentum
Explanation :
· The angular momentum of an object in rotational motion is the moment of linear momentum .
· Angular momentum equal to moment of inertia multipy by angular velocity
· In formulae we write as, L = Iω; where i=moment of inertia, ω=angular velocity
· The SI unit for the angular momentum is kg m2 s-1
· The conservation of angular momentum is states that the total angular momentum of a system about an axis of rotation constant if no external torque acts on the system where I ω = constant.
Question 1 :
Define angular momentum.
Answer :
Angular momentum is the moment of momentum and it is the vector product of the moment of inertia and angular velocity.
Question 2 :
Why a diver is able to somersault a number of times before hitting the water ?
Answer :
A diver is able to somersault a number of times before hitting the water because after the diver leaping off the diving board, the diver decreases his moment of inertia by bringing his hands and legs close together. So when the moment of inertia is decreases, the speed of rotation angular velocity ω is increases.
After that just before hitting the water, the diver straightens his limbs to increase the moment of inertia and angular velocity ω will be decreases.
So that by applying the principle of conversation of angular momentum, the total angular momentum of a system about an axis of rotation is constant if no external torque acts on the system, I ω = constant.
From that we can define the angular momentum of a body as the product of the moment of inertia I and the angular velocity ω.
Picture for theory of question 2
Question 3 :
By using conservation of angular momentum, differentiate between a raw egg from a hard-boiled egg by spinning the eggs on the table.
Answer :
· Raw egg : When the egg is spun, the yolk being denser move outwards. The moment of inertia I is increases but the angular velocity ω decreases rapidly. The egg spins a couple of revolutions only and the stops.
· Hard-boiled egg : When the egg is spun, the moment of inertia I remains unchanged because the yolk is fixed. But the angular velocity decreases slowly due to friction. Then the egg spins for a longer period.
So from that differentiate show that hard-boiled egg is related to conservation of angular momentum. This is because that conservation said angular momentum is , I ω = constant.
Picture for theory of question 3
Question 4 :
A particle of mass 500g is moving in a circular motion at an angular velocity of 20 rad s-1 . The radius of circular path is 12cm. Determine the angular momentum of this particle.
Angular momentum , L = Iω where I is moment of inertia, ω is angular velocity
= mr2ω where m is mass, r is radius of circular path, ω is angular velocity
So that :
= (500 x 10-3) ( 12 x 10-2)2 (20)
= 0.144 kg m2 s-1
