Torque on a rotating system system

In summary, the total moment of inertia of the system is calculated to be ##2ml²Sin²θ##, which leads to an angular momentum of ##2ml²ωSin²θ##. To determine the torque on the system, the angular momentum needs to be differentiated, but without any time dependent terms, the vertical component is the only one obtained. In order to see if the direction of angular momentum is changing, the vector definition for a point particle should be used with the origin at the center of the rod.
  • #1
Saptarshi Sarkar
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13
Homework Statement
A thin massless rod of length 2l has equal point masses m attached at its ends (see
figure). The rod is rotating about an axis passing through its centre and making angle θ with it. What is the magnitude of the rate of change of its angular momentum?
Relevant Equations
##L=Iω##
##τ=Iα=\frac {dL}{dt}##
IMG_20200206_001717.jpg


I calculated the total moment of inertia of the system to be ##2ml²Sin²θ##, so the angular momentum is ##2ml²ωSin²θ##.

To get the torque on the system I need to differentiate the angular momentum but I don't have any time dependent terms. What should I do?
 
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  • #2
Your expression gives only the vertical component of angular momentum. You’re going to need the vector expression for the total angular momentum in order to see if the direction of angular momentum is changing.

So, use the vector definition of angular momentum for a point particle. Take the origin at the center of the rod.
 
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What is torque on a rotating system?

Torque on a rotating system is the measure of the force that causes an object to rotate around an axis. It is also known as rotational force.

How is torque calculated?

To calculate torque on a rotating system, you need to multiply the force applied to the object by the distance from the axis of rotation. Mathematically, torque = force x distance.

What factors affect the torque on a rotating system?

The factors that affect torque on a rotating system are the magnitude of the force, the distance from the axis of rotation, and the angle between the force and the lever arm.

Can torque change the direction of rotation?

Yes, torque can change the direction of rotation. When the torque applied to an object is in the opposite direction to its current rotation, it can cause the object to rotate in the opposite direction.

How is torque on a rotating system used in real-world applications?

Torque on a rotating system is used in many real-world applications, such as engines, motors, and turbines. It is also essential in understanding the stability and balance of structures, such as bridges and buildings.

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