Question

A light rigid rod 1.00 m in length joins two particles, withmasses 4.00 kg and 3.00 kg, at its ends. The combination rotates inthe xy plane about a pivot through the center of the rod(Fig. P11.11). Determine the angular momentum of the system aboutthe origin when the speed of each particle is 6.40 m/s.

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  Figure P11.11

Answer 1

Concepts and reason

The problem deals with the concept of the angular momentum and right hand thumb rule as the magnitude and direction of the momentum of the rotating system is to be determined.

First determine the angular momentum of the rotating system using the formula of angular momentum then determine the direction of the angular momentum using the right hand thumb rule.

Fundamentals

The angular momentum of a system is defined as the product of linear momentum and distance between the pivot point and mass.

The angular momentum can be defined as:

$L=pxr $

The linear momentum is defined as the product of the mass and velocity as:

$p=mv $

Then the angular momentum is as:

Here is the direction of the angular momentum and is the distance between pivotal point and the mass and is the angle between the direction of motion and axis across which object is moving.

The right hand thumb rule is used to determine the direction of the angular momentum as the direction of angular velocity and angular momentum are perpendicular to the plane of rotation. Using the right hand rule, the direction of both angular velocity and angular momentum is defined as the direction in which the thumb of right hand points when curl fingers are in the direction of rotation.

Since both the objects of the system are moving in same direction so the net angular momentum of the system will be the addition of individual angular momentums.

The mass of first object is

The mass of second object is

The velocity of both the objects is

The distance for both the objects is

Consider the magnitude of the angular momentum of first object is and for second object then the net momentum will be:

For both the objects the angle $0=90° $ between the direction of motion and axis across which object is moving.

Substitute the mass of first object, mass of second object , velocity of both the objects and distance for both the objects $r=0.5m $Therefore the net momentum of the system is:

Both the masses are moving in the same direction i.e. counter clockwise.

So from the right hand thumb rule if the fingers of the right hand are curl in the direction of the movement of the system then the thumb will be out of the page.

Therefore the direction of the angular momentum will be out of the page i.e. direction

Ans:

The magnitude of the net momentum of the system is and the direction of the angular momentum will be out of the page i.e. direction.