A long thin rod of length L = 8m and mass 5.5 kg with a uniform mass density is laid parallel to the x-axis and is rotated about a y-axis at L = 3m. Calculate its Moment of Inertia
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 thin rod of length L and total mass M has a linear mass density that varies with position as λ(x)-γ?, where x = 0 is located at the left end of the rod and γ has dimensions M/L3. ĮNote: requires calculus] (a) Find γ in terms of the total mass M and the length L. (b) Calculate the moment of inertia of this rod about an axis through its left end, oriented perpen dicular to the rod; expressed...
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...
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...
(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...
1. Finding the Moment of Inertia of a Uniform Thin Rod with mass M and length L rotating about its center (a thin rod is a ID object; in the figure the rod has a thickness for clarity): For this problem, use a coordinate axis with its origin at the rod's center and let the rod extend along the x axis as shown here (in other problems, you will need to generate the diagram): dx dm Now, we select a...
(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 uniform thin rod of mass M- 4.27 kg pivots about an axis through its center and perpendicular to its L of the rod be so that the moment of inertia of the three-body system with respect to the described axis is I -0.983 kg m2? Number rm H7I 7i
Consider a thin rod of length L and mass M situated with one end at the origin x = 0 of the coordinate system as shown Mostly need help with part B. Thank you a) Four 1 kg boxes sit on a 5 m long uniform rod of mass 4 kg, such that the total mass of the system is 8 kg. The boxes are spaced 1 m apart, with the first box sitting at the left end of the...
A thin uniform rod (length = 1.77 m, mass = 3.13 kg) is pivoted about a horizontal frictionless pin through one of its ends. The moment of inertia of the rod through this axis is (1/3)mL2. The rod is released when it is 58.5° below the horizontal. What is the angular acceleration of the rod at the instant it is released? (in rad/s^2) A: 2.712 B: 3.173 C: 3.713 D: 4.344 E: 5.082 F: 5.946 G: 6.957 H: 8.140