Rotation of Planetary gears about a fixed Sun gear

In summary, the conversation discusses a specific and difficult coursework question involving finding the angular velocity of 2 planetary gears rotating about a larger Sun gear while attached to a quarter circle plate. The initial energy of the system is determined, but the process of finding the final kinetic energy is unclear due to the involvement of tangential gravity. However, it is noted that kinetic energy is based on geometry and does not involve forces.
  • #1
SugreF
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This coursework question I am faced with is very specific and quite difficult to explain so I have attached the question. The writing on the side is not that important so don't try and make sense of it.

The question asks to find the angular velocity of 2 planetary gears (which are connected by a quarter circle plate) rotating about a larger Sun gear. The plate is attached to the centre of the planetary gears at the corners where the arc and the radii meet, with the 2 radii converging at the centre of the Sun gear.

the mass of the 2 planetary gears are 2kg

the mass of the quarter circle is 6kg

the radius of the Sun gear is 0.15m

the radius of the planetary gears are 0.075m


things I worked out from that:

Radius of quarter circle = 0.225m

Centre of mass of the quarter circle = 0.135m from the pinnacle.


Initially, the quarter circle occupies quadrant 1 entirely, with the planetary gears connected at the corners.

The question asks to find the angular velocity of the planetary gears when the quarter circle moves through Pi/2 rad clockwise to occupy quadrant 4 entirely.



This is an energy conservation question, however I'm struggling with the relevant circular motions.

KE + PE + RE=constant

I found the centre of mass of the quarter circle and thus found the initial energy of the system but wasnt sure what to do next.


I want to find the final KE but I am not sure how to approach this. I know gravity is working tangentially to the Sun gear, but how do you incorporate that into the relevant KE equation?


Thanks in advance
 

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  • #2
Welcome to PF!

Hi SugreF! Welcome to PF! :smile:
SugreF said:
… I want to find the final KE but I am not sure how to approach this. I know gravity is working tangentially to the Sun gear, but how do you incorporate that into the relevant KE equation?

You don't …

KE is geometry, and has nothing to do with forces …

it's just 1/2 mvc.o.m.2 + 1/2 Ic.o.m.ω2, = 1/2 Ic.o.r.ω2 :wink:
 

1. What is meant by "Rotation of Planetary gears about a fixed Sun gear"?

"Rotation of Planetary gears about a fixed Sun gear" refers to a specific type of gear system where multiple smaller gears, known as planetary gears, rotate around a larger, fixed gear called the Sun gear. This type of gear system is commonly used in machinery and vehicles to transfer power and motion between different parts.

2. How does the rotation of planetary gears about a fixed Sun gear work?

The rotation of planetary gears about a fixed Sun gear works by utilizing the meshing of the gears' teeth. As the Sun gear remains stationary, the planetary gears rotate around it, causing the whole system to move. This allows for a transfer of power and movement between different components connected to the gears.

3. What are the advantages of using a rotation of planetary gears about a fixed Sun gear?

One advantage of this type of gear system is its compact size. By having the smaller planetary gears rotate around a fixed central gear, the overall size of the gear system can be reduced. Additionally, this type of gear system can handle high torque and has a high gear ratio, making it useful for heavy-duty applications.

4. Are there any limitations to the rotation of planetary gears about a fixed Sun gear?

One limitation of this type of gear system is that it is not as efficient as other gear systems, such as spur gears or helical gears. This is because the planetary gears have to rotate around the Sun gear, causing friction and reducing the overall efficiency of the system. Additionally, this type of gear system can be more complex and difficult to design and manufacture.

5. How is the rotation of planetary gears about a fixed Sun gear used in real-world applications?

The rotation of planetary gears about a fixed Sun gear is commonly used in various applications, such as automotive transmissions, industrial equipment, and even some household appliances. It allows for a compact and efficient transfer of power and motion, making it a popular choice in many industries.

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