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Moment of Inertia: Rotational Inertia of Solid Discs and Rods, Schemes and Mind Maps of Physics

Charlotte Technical CollegePhysics

Problem A. uniform thin rod of mass M and length L spins around a central axis that is perpendicular to its length.

Typology: Schemes and Mind Maps

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Moment of Inertia
Dr. M.E. Jamer
October 17, 2018
Problem 1. Determine the rotational inertia of a uniform solid disc of mass Mand radius Rspinning around its
center. (Answer: Idisc = 1/2M∗R2)
Problem A. uniform thin rod of mass M and length L spins around a central axis that is perpendicular to its
length. (a) What is the rotational inertia of this rod about this axis? (b) If this rod has a mass of 48 g and
length of 27 cm and it rotates with a period of 0.90 s, what is the ro ds rotational kinetic energy? (Answer:
Irod = (1/12) ∗M∗L2(aboutcenterof rod), K = 0.007106J)
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Moment of Inertia

Dr. M.E. Jamer

October 17, 2018

Problem 1. Determine the rotational inertia of a uniform solid disc of mass M and radius R spinning around its center. (Answer: Idisc = 1/ 2 M ∗ R^2 )

Problem A. uniform thin rod of mass M and length L spins around a central axis that is perpendicular to its length. (a) What is the rotational inertia of this rod about this axis? (b) If this rod has a mass of 48 g and length of 27 cm and it rotates with a period of 0.90 s, what is the rods rotational kinetic energy? (Answer: Ir od = (1/12) ∗ M ∗ L^2 (aboutcenterof rod), K = 0. 007106 J)

Problem A. thin uniform rod of length L and mass M is mounted non-centrally to an axle. Placing the x axis along the rod with the axle along the z axis, the rod extends from x = a to x = +b where a + b = L. (a) By altering the limits of integration in our previous analysis of the thin rod, find the rotational inertia I of the rod about this non-central axle? (b) Derive an alternate form for the result by application of the parallel-axis theorem. (Answers: Ir od = M ∗ (b^3 + a^3 )/(3 ∗ L) = (1/12) ∗ M ∗ L^2 + M ∗ [(b − a)/2]^2 )