Calculate by direct integration the moment of inertia for a thin rod of mass M and length L about an axis located distance d from one end.
Calculate by direct integration the moment of inertia for a thin rod of mass M and length L about an axis located distance d from one end. Express your answer in terms of the given quantities. I = ________________________
Homework Answers
Add Answer to:
Calculate by direct integration the moment of inertia for a thin rod of mass M and length L about an axis located distance d from one end.
1. A thin rod of length L and total mass M has a linear mass density...
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...
A very thin, straight, uniform rod has a length of 3.00 m and a total mass...
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...
Consider a thin rod of length L and mass M situated with one end at the...
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...
1. a. A very thin, straight, uniform rod has a length of 3.00 m and a...
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...
(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...
L- Pivot Point 13.) A uniform, thin rod of length L and mass M is allowed to pivot about its end,...
L- Pivot Point 13.) A uniform, thin rod of length L and mass M is allowed to pivot about its end, as shown in the figure above (a) Using integral calculus, derive the rotational inertia for the rod around its end to show that it is ML2/3 The rod is fixed at one end and allowed to fall from the horizontal position A through the vertical position B. (b) Derive an expression for the velocity of the free end of...
(a) Knowing that the moment of inertia of a thin uniform metallic rod of mass m...
(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...
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...
Three identical thin rods, each of length L an mass m, are welded perpendicular to one...
Three identical thin rods, each of length L an mass m, are welded perpendicular to one another as shown in Figure P10.23. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another Determine the moment of inertia of this structure. (Answer in terms of m and L.) Axis of rotationn Figure P10.23
Calculate the moment of inertia of the following figure about the axis O. A is a...
Calculate the moment of inertia of the following figure about
the axis O. A is a uniform solid cylinder with mass M and radius R.
B is a uniform thin rod with mass M and length 3R. A and B objects
are attached together and rotate together about axis O. The
distance X is and Y is in the figure. The
light blue line is going through the center of the cylinder and the
point “CM” represents the center of mass of...
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...
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...
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...
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...
L- Pivot Point 13.) A uniform, thin rod of length L and mass M is allowed to pivot about its end, as shown in the figure above (a) Using integral calculus, derive the rotational inertia for the rod around its end to show that it is ML2/3 The rod is fixed at one end and allowed to fall from the horizontal position A through the vertical position B. (b) Derive an expression for the velocity of the free end of...
(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...
Three identical thin rods, each of length L an mass m, are welded perpendicular to one another as shown in Figure P10.23. The assembly is rotated about an axis that passes through the end of one rod and is parallel to another Determine the moment of inertia of this structure. (Answer in terms of m and L.) Axis of rotationn Figure P10.23
Calculate the moment of inertia of the following figure about
the axis O. A is a uniform solid cylinder with mass M and radius R.
B is a uniform thin rod with mass M and length 3R. A and B objects
are attached together and rotate together about axis O. The
distance X is and Y is in the figure. The
light blue line is going through the center of the cylinder and the
point “CM” represents the center of mass of...
Most questions answered within 3 hours.
-
Why would natural selection not minimize costs (in the form of
symptoms) of evolved defenses? (choose...
asked 4 minutes ago -
What is true about a critical task?
Latest finish time - latest start time = 0...
asked 6 minutes ago -
A company uses a
process costing system. Its Assembly Department's beginning
inventory consisted of 56,800 units,...
asked 6 minutes ago -
a
sealed glass cylinder contains 325 g of N2 gas at 1.02 atm at 20 c....
asked 11 minutes ago -
The main difference between an equity and a nonequity alliance
is that
A
equity alliances are...
asked 9 minutes ago -
Need help with this, in JAVA, using netbeans. A
complete response will receive a positive comment...
asked 17 minutes ago -
An imprest petty cash fund of $600 was established for minor
disbursements. At the end of...
asked 22 minutes ago -
Sharpe Cutter is a small company that produces specialty knives
for paper cutting machinery. The annual...
asked 27 minutes ago -
Calculating the Ka of a weak acid from
pH:
The pH of a 0.68M solution of...
asked 28 minutes ago -
1.What process is pushing back against gravity in the very
center (the core) of sun-like stars?...
asked 48 minutes ago -
This question is from the textbook "Python for ArcGIS" by Laura
Tateosian:
Write a script "triangles.py"...
asked 46 minutes ago -
Which of the following is an impediment that makes it
difficult for firms to achieve the...
asked 47 minutes ago