Lever and Acceleration: Greater Mass or Greater Accel?

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SUMMARY

The discussion centers on the mechanics of levers, specifically a 10m lever with its center of mass 2m from the right side. It establishes that for the lever to maintain balance, the shorter arm must possess greater mass. The gravitational acceleration is uniform across both arms, negating the idea that the longer, lighter arm experiences greater acceleration due to traveling a longer distance. The conversation concludes that additional unbalanced torque is necessary to induce acceleration in the lever, resulting in uniform angular acceleration across both arms while varying linear accelerations at their endpoints.

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  • Understanding of basic physics principles, particularly levers and torque.
  • Familiarity with concepts of gravitational acceleration and mass.
  • Knowledge of angular acceleration and its relationship to linear acceleration.
  • Basic geometry related to lever arms and distances.
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  • Study the principles of torque and its effect on lever systems.
  • Explore the relationship between mass distribution and balance in levers.
  • Learn about angular acceleration and its implications in rotational dynamics.
  • Investigate the geometry of levers and how it affects linear acceleration at endpoints.
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ultrauser
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If I have 10m lever with a center of the mass 2m from the right side it must mean the shorter arm have greater mass to keep balance. Does it mean longer (lighter) arm have greater gravitational acceleration cause it must travel greater distance in the same time ?
 
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ultrauser said:
If I have 10m lever with a center of the mass 2m from the right side it must mean the shorter arm have greater mass to keep balance.
Only if it is in balance - a lever does not have to balance.

Does it mean longer (lighter) arm have greater gravitational acceleration cause it must travel greater distance in the same time ?
No.
1. the acceleration of gravity is the same for all masses anyway
2. since the two sides are in balance, the force due to gravity on both sides is the same - it cannot be accelerating: so you have a contradiction in your statement.

Notes:
In order to accelerate the lever, you need an additional unbalanced torque.
That torque causes the same angular acceleration in both arms.
The linear/tangential acceleration varies along the length of each arm - and is the same (with opposite sign) at equal lengths. The difference in linear accelerations of the endpoints is due to geometry.
 

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