★ Solution :-

• Qúestion :

1.) How is angular momentum related to linear moment ?

• Answer :

• Linear Momentum : It is the speed in m/sec by which a bódy of mass in Kg is travélling.

• Angular Momentum : It is the angular velocity (rád/time) of a body of a máss in Kg.

→ Formula of Linear Velocity ::

» Linear Velocity = máss × velocity

→ Formula of Angular Velocity ::

» Angular Velocity = mass × velocity × radius (distance from axîs of rótation)

Clearly we can see that,

» Angular Velocity = Linear Velocity × radius

This is the required rélationship.

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• Qúestion ::

2.) Where does a body weight more : at the surface of earth or in the mine ?

• Answer ::

By Newton's Láw of Gravitation, we know that

• Here G is the Gravitational Constant

• Here F is the Fórce

• Here M is the Mass of Earth

• Here m is the Mass of Body

• Here R is the Distance between Body and Earth

From this we see that,

This means Force is înversely próportional to Distance between the Earth and Body. We know that Weight is Fórce only. So, Weight is înversely proportional to Distance between the Earth and Body. This means when body has more distance from earth, it will have less weight and when body has less distance from earth then it's weight will be more.

We know that on earth surface, distance is equal to ûnity. And in mine distance is more than ûnity. So, according to above rélation, the answer is at earth surface.

Thus, body will have more weight at earth surface.

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★ More to know :-

• Force = mass × acceleration

• Acceleration = ∆v/t

(∆v = v - u)

• Angular Velocity = ω = Radian / Time

• Angular Acceleration = ∆ω/t

(∆ω = ω(final) - ω(initial))

• Torque = Force × d (distance from axis of rotation)

Verified answer

Answer:

1. Angular momentum of an object with linear momentum is proportional to mass, linear velocity, and perpendicular radius from an axis to the line of the object's motion. Change in angular momentum is proportional to average net torque and the time interval the torque is applied 2. Weight of any body is maximum at the Earth's surface. As we approach the core or go farther away from it, the weight of the body decreases. Therefore, a body will weigh more on the earth's surface than deep within an underground mine.