Rotational Motion with a Suspended Hinge

AI Thread Summary
A thin rod of mass 0.490 kg and length 1.16 m is suspended from a hinge and subjected to a horizontal impulsive force of 12.7 N. The discussion focuses on calculating the acceleration of the center of mass when the force is applied at the bottom and midpoint of the rod, as well as determining the hinge's horizontal reaction force. Participants suggest using the net force equation and the relationship between torque, moment of inertia, and angular acceleration to solve the problem. The concept of the center of percussion is also introduced, where the impulse can be applied without exerting horizontal force on the hinge. The conversation highlights the need for a clearer understanding of the physics involved to tackle the problem effectively.
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The Problem:
A thin rod of mass 0.490 kg and length 1.16 m is at rest, hanging vertically from a strong, fixed hinge at its top end. Suddenly, a horizontal impulsive force (12.7) N is applied to it.
a) Suppose the force acts at the bottom end of the rod. Find the acceleration of its center of mass.
(b) Find the horizontal force the hinge exerts.
(c) Suppose the force acts at the midpoint of the rod. Find the acceleration of this point.
(d) Find the horizontal hinge reaction force.
(e) Where can the impulse be applied so that the hinge will exert no horizontal force? This point is called the center of percussion.

2. Homework Equations
Fnet=ma
Fnet=m(accelertaiton of center of mass)

3. The Attempt at a Solution
I attempted to use the Fnet equation to solve for the acceleration but I got the wrong answer. I'm nor sure how to fiqure out the parts b or d and I'm sure that once I fiqure our part a part c wil be fairly easy. I'm kinda running around in circles with this problem. If someone could just give me a jumping off point, not necessarily the answer, i would greatly appreciate it. Thanks!
 
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Use the relation torque = moment of inertia times angular acceleration, too.

ehild
 
Last edited:
Thank you very much , that helped a lot! It was that push in the right direction that I needed.
 
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