Angular Momentum of Rotational Dynamics System

In summary, a 0.14 meter long, 0.15 kg rigid rod with a 0.22 kg mass on one end and a 0.080 kg mass on the other rotates at 1.7 rad/s without friction. The magnitude of the angular momentum of the system, taking the center of the rod as the origin, can be calculated using the equation L = Iω, where I is the moment of inertia and ω is the angular velocity. The moment of inertia of the system can be calculated by adding the moment of inertia of the rod (1/12mL^2) and the moment of inertia of the two point masses. Therefore, the final equation
  • #1
linnus
23
0

Homework Statement



0.14 meter long, 0.15 kg thin rigid rod has a small 0.22 kg mass stuck on one of its ends and a small 0.080 kg mass stuck on the other end. The rod rotates at 1.7 rad/s through its physical center without friction. What is the magnitude of the angular momentum of the system taking the center of the rod as the origin? Treat the masses on the ends as point masses.

Homework Equations



I= summation of mr^2
I=1/12mL^2 (for the rod)
L=IW

The Attempt at a Solution


I=1/12(.45)(.14^2)= .000735
L=.000735 (1.7)=.0012495 kgm/s^2
 
Last edited:
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  • #2
physical center? is that center of mass or something? or midway of rod?

there is contribution from the small masses to moment of inertia
 
  • #3
I think it means the midway of the rod.
 
  • #4
either way you will need to include the two point masses at the two ends
 

Related to Angular Momentum of Rotational Dynamics System

1. What is angular momentum?

Angular momentum refers to the measure of an object's rotational motion, taking into account its mass, velocity, and distance from the axis of rotation. It is a vector quantity, meaning it has both magnitude and direction, and is often denoted by the symbol "L".

2. How is angular momentum calculated?

The formula for calculating angular momentum is L = Iω, where L is the angular momentum, I is the object's moment of inertia (a measure of its resistance to rotational motion), and ω is the angular velocity (the rate at which the object is rotating).

3. What is the conservation of angular momentum?

The law of conservation of angular momentum states that in a closed system (where no external torques are acting), the total angular momentum remains constant. This means that if one part of the system gains angular momentum, another part must lose an equal amount in the opposite direction.

4. How does angular momentum affect rotational motion?

Angular momentum is directly related to an object's rotational motion. When there is no external torque acting on a rotating object, its angular momentum remains constant. This means that as the moment of inertia changes (due to a change in shape or distribution of mass), the angular velocity must also change to maintain the same angular momentum.

5. What are some real-life applications of angular momentum?

Angular momentum has many practical applications, such as in the design of vehicles and machinery, understanding the behavior of spinning objects (such as tops and gyroscopes), and analyzing the motion of celestial bodies. It is also important in sports, such as figure skating and gymnastics, where rotating bodies perform intricate movements.

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