Exercise
https://texercises.com/exercise/oscillating-rod/
Question
Solution
Short
Video
\(\LaTeX\)
No explanation / solution video to this exercise has yet been created.

Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
A cylindrical rod with length hO and radius rO rotates about one of its s with an amplitude AO. abcliste abc Calculate the oscillation period. abc Calculate the velocity of the lower tip of the rod when it passes the equilibrium position. abcliste

Solution:
abcliste abc The rod corresponds to a physical pulum with a moment of inertia with respect to the centre of mass of the rod J_s mleftfracr^+frach^right It follows for the period T &approx pisqrtfracJ_s+m s^m g s pisqrtfracmleftfracr^+frach^right+m h/^m g h/ pisqrtfracleftfracr^+frach^right+frach^g h/ pisqrtfracleftfracr^+frach^rightg h TF pisqrtfractimesr^+timesh^timesncgtimesh T approx resultTP abc The lower tip of the rod moves with a velocity vth dotphit. The maximum of this velocity is given by sscvmax homegahatphi where hatphi is the angular amplitude of the oscillation. It follows that sscvmax hfracpiThatphi sqrtfracghr^+h^ hhatphi vmaxF sqrtfractimesncgtimeshtimesr/h^+timesArad vmax approx resultvmaxP abcliste
Meta Information
\(\LaTeX\)-Code
Exercise:
A cylindrical rod with length hO and radius rO rotates about one of its s with an amplitude AO. abcliste abc Calculate the oscillation period. abc Calculate the velocity of the lower tip of the rod when it passes the equilibrium position. abcliste

Solution:
abcliste abc The rod corresponds to a physical pulum with a moment of inertia with respect to the centre of mass of the rod J_s mleftfracr^+frach^right It follows for the period T &approx pisqrtfracJ_s+m s^m g s pisqrtfracmleftfracr^+frach^right+m h/^m g h/ pisqrtfracleftfracr^+frach^right+frach^g h/ pisqrtfracleftfracr^+frach^rightg h TF pisqrtfractimesr^+timesh^timesncgtimesh T approx resultTP abc The lower tip of the rod moves with a velocity vth dotphit. The maximum of this velocity is given by sscvmax homegahatphi where hatphi is the angular amplitude of the oscillation. It follows that sscvmax hfracpiThatphi sqrtfracghr^+h^ hhatphi vmaxF sqrtfractimesncgtimeshtimesr/h^+timesArad vmax approx resultvmaxP abcliste
Contained in these collections:

Attributes & Decorations
Branches
Harmonic Oscillations
Tags
period, physical pendulum
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration
File
Link