Physics Problem Involving Moment and Acceleration

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SUMMARY

The discussion focuses on calculating the tangential acceleration of the outer tip of a uniform board of length L, hinged at its lower end and released from an angle θ above the horizontal. Participants emphasize the importance of considering rotational kinetic energy and the moment of inertia in the calculations. The correct approach involves analyzing the forces and torques acting on the board as it transitions through the horizontal position. The tangential acceleration is directly related to the gravitational force acting on the board.

PREREQUISITES
  • Understanding of rotational dynamics and moment of inertia
  • Familiarity with kinetic energy equations, including rotational kinetic energy
  • Basic knowledge of torque and angular acceleration
  • Concept of gravitational force acting on rigid bodies
NEXT STEPS
  • Study the equations of motion for rigid bodies in rotational dynamics
  • Learn about calculating moment of inertia for different shapes
  • Explore the relationship between torque, angular acceleration, and tangential acceleration
  • Investigate conservation of energy principles in rotational systems
USEFUL FOR

Students of physics, mechanical engineers, and anyone interested in understanding the dynamics of rotating bodies and the application of torque in real-world scenarios.

taylorkrauss
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A uniform board length L hinged about its lower end, held at θ above the horizontal is released from rest. As it passes through the horizontal what is the tangential acceleration of its outer tip?



At first when I attempted this, I applied conservation of energy.
(1/2)mv^2+mgh=(1/2)mv^2 + mgh
but I did not get an answer.
Then I decided could the answer just be L*gravity?? Any help given will be much apreciated! Thank you!
 
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welcome to pf!

hi taylorkrauss! welcome to pf! :smile:

your kinetic energy must include the rotational KE:

KE = 1/2 mvc.o.m2 + 1/2 Ic.o.mω2 = 1/2 Ic.o.rω2 :wink:​
 
You're looking for tangential acceleration, not velocity. So think about the moment of inertia, where the center of rotation is, and what forces are acting to produce a torque at the instant in question.
 

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