Original :
Sebuah silinder dikaitkan pada sebuah pegas dengan konstanta k sedang ujung lain pegas di tahan tetap. Sistem silinder pegas ini di letakkan pada bidang datar horizontal kasar sehingga silinder bisa menggelinding tanpa slip. Jika momen inersia silinder bermassa M adalah 1/2 MR^2 dan silindernya mempunyai jari-jari R, maka besar periode pusat massa silinder adalah...
Translated :
A cylinder is attached to a spring with constant k, while the other end of the spring is remain fixed (e.g. :at wall). Spring cylinder system is place on rough horizontal plane so that the cylinder can roll without slipping. If the moment of inertia of the cylinder with mass M is 1/2 MR ^ 2 and the cylinder has a radius R, then the period of the center of mass of the cylinder is the ...
Answer :
Because no image I will try to explain the image descriptively. The right end of spring is attached fix to wall and the left end of spring is attached to cylinder. The cylinder is swinging horizontally (left and right) on horizontal plane. The swing is cause by spring which attached to cylinder. While swinging left-right the cylinder is rotating, repeatedly rotate clockwise(to right) then counter-clockwise(to left) and back again clockwise(to right side) (rotate because rough plane).
The cylinder will have two kind of move, one is translation and second is rotation. This can be solve similarly as swinging block which attached to a spring (that neglect the plane resistance).
Because this system consist of two kind of move, then let's start from two point. First is Newton's Law of Force "sum of Force is equal to mass multiply acceleration" (left side) [this for translation movement] and second is "sum of Torque equal to inertia of moment multiply angular acceleration." (right side) [this for rotating movement]
In sum of horizontal force, consist of force of spring and resistance force. For force of spring just substitute Hooke's Law. But for resistance force, not came from zero sum of vertical force like you do in non-rotating system (a system that just contain translation movement). Instead the resistance force came from total torque.
In total torque, only resistance force that give effect on rotating the cylinder (the weight and the Normal force of plane didn't give any effect on rotation, because the those force pierce through center of rotation, so zero distance from turning point to force). From here you got the resistance force value in term of mass and acceleration.
Now back to sum of horizontal force, substitute the resistance force that you got earlier. and substitute the linear acceleration (with a formula for relation between linear acceleration and angular velocity). There you got the angular velocity and substitute again the angular velocity with period related formula.
After done some algebra math operation, you got the period in term of mass and spring constant.
Thank you for paying attention.. ^^
Happy Expressing..!!
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