Maximum Rotational Speed for Bar with Masses on Ends

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SUMMARY

The discussion centers on calculating the maximum rotational speed of a bar with masses attached to its ends, specifically a 35.1-cm-long bar with 1.81-kg masses. The maximum force supported by the screws is 70.3 N. The initial calculation for linear velocity (v) yielded approximately 3.69226 m/s, but this was questioned in relation to whether the problem actually sought the maximum angular velocity instead. The distinction between linear and angular velocity is crucial for accurate problem-solving in rotational dynamics.

PREREQUISITES
  • Understanding of Newton's 2nd Law
  • Familiarity with centripetal acceleration and its formula (a_rad = v^2/r)
  • Knowledge of rotational dynamics and angular velocity
  • Basic principles of forces acting on rotating bodies
NEXT STEPS
  • Study the relationship between linear velocity and angular velocity in rotational systems
  • Learn how to apply Newton's 2nd Law to rotational dynamics problems
  • Explore examples of centripetal force calculations in different contexts
  • Investigate the effects of gravitational forces on rotating objects
USEFUL FOR

Students in physics, mechanical engineers, and anyone involved in dynamics and rotational motion analysis will benefit from this discussion.

usamo42j
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Homework Statement


A machine part consists of a thin 35.1-cm-long bar with small 1.81-kg masses fastened by screws to its ends. The screws can support a maximum force of 70.3 N without pulling out. This bar rotates about an axis perpendicular to it at its center.


Homework Equations


Newton's 2nd law, a_rad=v^2/r


The Attempt at a Solution


(What am I doing wrong?)
The centripetal acceleration is v2/r=v2/0.351 m/s^2, so the net force on each mass is 1.81v^2/0.351 N ≤ 70.3 N

Solving we get v ≤ ~3.69226 m/s, so the largest v is that.

However, I'm being told this is wrong. However, the same problem with very similar numbers but different numbers had an answer of ~3.61 which is pretty close.
 
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Are you sure http://en.wikipedia.org/wiki/Centripetal_force" is the right force?

Gravity is attempting to pull the weight down, which would turn the bar.

If the bar turned, the weight would get closer to the axis of rotation.

Is there a force that might be against the weight getting any closer to the axis of rotation?

;)
 
Last edited by a moderator:
usamo42j,

What you have done seems to be correct, that is, if you were asked the maximum speed of the masses.

Are you sure it doesn't ask for the maximum rotational speed (angular velocity) ?
 

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