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QUESTION: 1

Two discs of moments of inertia I_{1} and I_{2} about their respective axes (normal to the disc and passing through the centre), and rotating with angular speeds I_{1} and I_{2} are brought into contact face to face with their axes of rotation coincident. What is the angular speed of the two disc system?

Solution:

As there is no any external force acting between the two discs so according to law of conservation of angular momentum, we get

L= Iω

So, I1ω1 + I2ω2 = (I1 + I2) ω

QUESTION: 2

Which of the following doesn’t use the application of Conservation of Angular Momentum?

Solution:

Conservation of angular momentum is one of the key conservation laws in physics, along with the conservation laws for energy and (linear) momentum. All the top 3 options use the application conversion of angular momentum.

But the cause of fruit drop can occur due to many reasons such as a severe pest infestation can stress the tree enough to cause fruit drop, Sudden changes in temperature, particularly when high temperatures occur at or shortly after fruit set, can cause fruit drop.

QUESTION: 3

Space craft orientation is based on the principle of:

Solution:

Conservation of angular momentum is a physical property of a spinning system such that its spin remains constant unless it is acted upon by an external torque; put another way, the speed of rotation is constant as long as net torque is zero.

QUESTION: 4

What is the relation between torque and angular momentum?

Solution:

QUESTION: 5

A circus acrobat while performing spins brings his limbs closer to the body. Due to this

Solution:

While in the pike position the body decreases in radius as each segment moves closer to the axis of rotation, resulting in angular velocity increasing and a decrease of moment of inertia. Thus, during a dive, angular momentum is constant meaning that moment of inertia is inversely proportional to angular velocity.

QUESTION: 6

An earth satellite is moving around the earth in a circular orbit. In such case, what is conserved?

Solution:

Angular Momentum is conserved

Mvr = constant

We can say that v is proportional to 1/r. When satellite stays near earth then velocity of the satellite is maximum.

QUESTION: 7

A child can balance himself on a moving cycle than on a stationary cycle. Based on

Solution:

Spinning wheels have angular momentum, and when you're sitting on a bike, you and it and its wheels make up a system that obeys the principle of conservation of angular momentum.

QUESTION: 8

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

Solution:

Angular momentum is conserved.

I1w1 = I2w2

I2 = (2/5)I1

I1(40) = (2/5)I1w2

w2 = 100 rpm

QUESTION: 9

A circus acrobat while performing spins brings his limbs closer to the body. Due to this

Solution:

Because when the moment of inertia decreases, rotational kinetic energy increases as work is done in decreasing the moment of inertia of the body.

A circus acrobat performs feats involving spin by bringing his arms and legs closer to his body or vice versa. On bringing the arms and legs closer to the body, his moment of inertia decreases. Hence his angular velocity increases. The reverse is also true.

QUESTION: 10

In system international, angular momentum is measured in

Solution:

L=Iω^{2}(L- angular momentum)

I(moment of inertia)=mr^{2}

L=1×1×100/60

L=1.6 kgm^{2}s^{-1}

≈1.9 kgm^{2}s^{-1}

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