Calculating Inertia and Kinetic Energy of Connected Shafts

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SUMMARY

The discussion focuses on calculating the moment of inertia, final speed, angular torque, and kinetic energy of two connected shafts during machine operation. Shaft 1, with a mass of 35 kg and a radius of gyration of 375 mm, has a moment of inertia of 4.62 kg·m². Shaft 2, with a mass of 45 kg and a radius of gyration of 520 mm, has a moment of inertia of 12.17 kg·m². The final speed of the connected shafts is determined to be 57.9 rad/s, and the angular torque required to increase the speed to 900 rev/min over 3.2 seconds is calculated based on the combined inertia of both shafts.

PREREQUISITES
  • Understanding of rotational dynamics and moment of inertia calculations
  • Familiarity with angular velocity and its conversion from revolutions per minute (rev/min)
  • Knowledge of kinetic energy formulas for rotating bodies
  • Basic grasp of torque and its relationship to angular acceleration
NEXT STEPS
  • Study the calculation of moment of inertia for composite bodies
  • Learn about angular momentum conservation in connected systems
  • Explore the relationship between torque, angular acceleration, and time
  • Investigate kinetic energy calculations for rotating systems
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Mechanical engineers, physics students, and anyone involved in the design and analysis of rotating machinery will benefit from this discussion.

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Homework Statement



b) During the operation of a machine, two shafts rotate in opposite directions and are then connected by a clutch system. Shaft 1 has a rotational speed of 800 rev/min, a mass of 35 kg and a radius of gyration of 375 mm. Shaft 2 has a rotational speed of 1100 rev/min, a mass of 45 kg and a radius of gyration of 520 mm. Determine:

i) the moment of inertia for each shaft;
ii) the final speed and direction of rotation for the connected shafts;
iii) the angular torque developed by the connected shafts if the rotational speed increases to 900 rev/min in a time of 3.2 s.
iv) the kinetic energy of the connected shafts at the increased speed.

Homework Equations



I1=m1k1squared
w3= 2pieN/60


The Attempt at a Solution



i. calculate I(1)=m1k1squared answers were 4.62 kgm2 & 12.17 kgm2
ii anti clockwise 57.9 rad/s with N3 working out 552.9 rev/min

iii not sure what changes speed here is it full speed combined or just shaft 1 ? Think I know how to do the rest when this is solved
 
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username0194 said:
is it full speed combined or just shaft 1 ?=
It says 'connected', so I would take it as the two shafts combined.
 

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