A rod with length L and mass L is pivoted about a horizontal, frictionless pin t

Question

A rod with length L and mass L is pivoted about a horizontal, frictionless pin through one end. It is released from rest with its center directly above the pivot point and rotates clockwise about the pin. Consider the instant its orientation is horizontal as shown.

https://s3.amazonaws.com/answer-board-image/7b57cd6ea27adb3e0c66a04753bdc4aa.jpg

1) Does the moment of inertia of the rod about the pivot point (a) increase, (b) decrease, or (c) remain the same as the rod rotates from the vertical to the horizontal orientation? Explain.
2) Does the magnitude of the torque on the rod due to its weight about the pivot point ((a) increase, (b) decrease, or (c) remain the same as the rod rotates from the vertical to the horizontal? Explain.
3) Does the magnitude of the angular acceleration of the rod about the pivot point (a) increase, (b) decrease, or (c) remain the same as the rod rotates from the vertical to the horizontal? Explain.
4) Does the magnitude of the angular momentum of the rod about the pivot point (a) increase, (b) decrease, or (c) remain the same as the rod rotates from the vertical to the horizontal orientation? Explain.
5) Does kinetic energy of the rod (a) increase, (b) decrease, or (c) remain the same as the rod rotates from the vertical to the horizontal orientation? Explain.
6) Does the gravitational potential energy of the rod (a) increase, (b) decrease, or (c) remain the same as the rod rotates from the vertical to the horizontal orientation? Explain.

Please pick a, b, or c and also explain – grading is based on 50% multiple choice and 50% explanation.

Thank you in advance!!!!!!!!!!!!!!!!!!

Explanation / Answer

1) Does the moment of inertia of the rod about the pivot point (c) remain the same as the rod rotates from the vertical to the horizontal orientation? Explain. moment ò inertia is only depend on mass and length of the rod, so there is no reason it ll change in the process 2) Does the magnitude of the torque on the rod due to its weight about the pivot point (b) decrease, ? Explain. torque on the rod due to its weight T=mg*L*sinalpha/2 because alpha is decresing as the rod swing from the initial position to the bottom point so that T is decreased. 3) Does the magnitude of the angular acceleration of the rod about the pivot point (b) decrease, Explain. we have that angular acceleration w=T/I where T be torque of weight, I be moment of inertia because T is decreased so w is decreased also. 4) Does the magnitude of the angular momentum of the rod about the pivot point (a) increase, Explain. because angular momentum P=I*w the angular acceleration is always positive so w always increase in magnitude so P is increase 5) Does kinetic energy of the rod (a) increase, Explain. becuase w is increase and K=I*w^2/2 so K is increase. 6) Does the gravitational potential energy of the rod (b) decrease, Explain. energy is conserved so kinetic + potential = constants kinetic is increase so potential is decrease.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.