MOI of rod about center axis = ML^2 / 12 = 4.27 * (L^2)/12
MOI of objects = MR^2 + MR^2 = > 2 * (0.593)* (L/2)^2
2 * (0.593)* (L/2)^2 + 4.27 * (L^2)/12 = 0.983
2 * (0.593)* (1/4) * (L)^2 + 4.27 * 1/12 * (L^2) = 0.983
L = 1.22m
A uniform thin rod of mass M- 4.27 kg pivots about an axis through its center...
A very thin, straight, uniform rod has a length of 3.00 m and a total mass of 7.00 kg. Treating the rod as essentially a line segment of mass (distributed uniformly), do the following: (i) Use integration to prove that the rod's center of mass is located at its center point. (Reminders: dmnds mass (and that axis is perpendicular to the rod). with the previous result-to calculate lemr the moment of inertia of the rod about an axis through one...
1. a. A very thin, straight, uniform rod has a length of 3.00 m and a total mass of 700 kg. Treating the rod as essentially a line segment of mass (distributed uniformly), do the following: (i) Use integration to prove that the rod's center of mass is located at its center point. ii) Now use integration to calculatethe moment of inertia of the rod about an axis through that center of (ii) Now use two different methods-first by direct...
An object is formed by attaching a uniform, thin rod with a mass of mr = 7.31 kg and length L = 5.68 m to a uniform sphere with mass ms = 36.55 kg and radius R = 1.42 m. Note ms = 5mr and L = 4R. *What is the moment of inertia of the object about an axis at the left end of the rod? *If the object is fixed at the left end of the rod, what...
A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass. The axis is perpendicular to the disk. The moment of inertial for the disk with a central axis is I MR2. Two non-rotating smaller disks, each with mass M2 and radius R/4, are glued on the original disk as shown in the figure. (a) Show that the ratio of the moments of inertia is given by I'/I = 35/16, where I' is the moment...
An object is formed by attaching a uniform, thin rod with a mass of m-7.28 kg and length L-5.64 m to a unlform sphere with mass ms-36.4 kg and radius R-1.41 m. ?te ms-5m, and L-4R. ) What is the moment of inertia of the object about an axis at the left end of the rod? g-m2 Submit You currently have O submissions for this question. Only 9 submisslon are allowed. You can make 9 more submissions for this question....
The moment of inertia of the human body about an axis through its center of mass is important in the application of biomechanics to sports such as diving and gymnastics. We can measure the body's moment of inertia in a particular position while a person remains in that position on a horizontal turntable, with the bodys center of mass on the turntable's rotational axis. The turntable with the person on it is then accelerated from rest by a torque that...
(a) Knowing that the moment of inertia of a thin uniform metallic rod of mass m and length L about an axis through its center of mass is (1/12) ml?, what is its moment of inertial about a parallel axis through one of its ends (show your calculation). (b) A physical pendulum consisting of a thin metallic rod of mass m = 200.0 g and of length L = 1.000 m is suspended from the upper end by a frictionless...
A thin uniform rod (mass = 0.440 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.65 s and an angular amplitude of 10.2°. What is the length of the rod? What is the maximum kinetic energy of the rod as it swings?
A thin uniform rod (mass = 0.16 kg) swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period of 1.7 s and an angular amplitude of 4.3 degree . (a) What is the length of the rod? (a) What is the maximum kinetic energy of the rod as it swings?
In the figure, a thin uniform rod (mass 4.6 kg, length 5.0 m) rotates freely about a horizontal axis A that is perpendicular to the rod and passes through a point at a distance d = 1.4 m from the end of the rod. The kinetic energy of the rod as it passes through the vertical position is 18 J. (a) what is the rotational inertia of the rod about axis A? (b) what is the (linear) speed of the...