Moment of Inertia: Motor, Shaft Speed & Torque Calculation

In any case, I think providing a summary of the conversation is the best approach for now. Here is the summary: In summary, the conversation discusses a motor with a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. It is connected to a shaft with a counter rotation of 600 rev/min through a clutch. The shaft has a mass of 80 kg and a diameter of 1200 mm. The common speed of rotation of the two shafts is found after slippage has finished, and the change in angular momentum and kinetic energy of the motor are determined as the common speed is reached. Finally, the time it takes for the motor to regain optimum running speed is calculated
  • #1
Busybee12
6
0
The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of 80 kg and a solid diameter of 1200 mm.

i) Find the common speed of rotation of the two shafts, immediately after slippage has finished.
ii) Determine the change in angular momentum of the motor as the common speed is reached.
iii) Determine the change in angular kinetic energy of the motor as the common speed is reached.
iv) If the motor sends a torque of 220 Nm, find how long it will take for the system to regain optimum running speed for the motor.

I have tried using equations but had no success
 
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  • #2
Hello and welcome to MHB! :D

Busybee said:
...I have tried using equations but had no success

It would be useful for our helpers to see which equations you used and how you attempted to apply them. Then perhaps it can be found where you may be going astray.
 

1. What is moment of inertia?

Moment of inertia, also known as rotational inertia, is a measure of an object's resistance to changes in its rotational motion. It is calculated by multiplying the mass of an object by the square of its distance from the axis of rotation.

2. How does moment of inertia affect motor performance?

The moment of inertia of a rotating object affects how quickly it can accelerate or decelerate, as well as how much torque is required to change its speed. A higher moment of inertia means more torque is needed to change the object's speed, which can impact the performance of a motor.

3. What factors affect moment of inertia?

The moment of inertia of an object depends on its mass, shape, and distribution of mass relative to the axis of rotation. Objects with larger masses or more spread out masses have a higher moment of inertia.

4. How do you calculate moment of inertia?

The moment of inertia can be calculated using the formula I = mr², where I is the moment of inertia, m is the mass of the object, and r is the distance from the axis of rotation.

5. How do you use moment of inertia to calculate shaft speed and torque?

The equation T = Iα can be used to calculate torque, where T is the torque, I is the moment of inertia, and α is the angular acceleration. This can be rearranged to find the angular acceleration, which can then be used in the equation ω = ω0 + αt to calculate the shaft speed at a given time t.

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