A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body.
Q: A disk with rotational inertia of I = 7.3 kg.m² and radius r = 32 cm, is initially at rest, but is…
A:
Q: a uniform mass density. C
A: (i) To show that all three principal moments of inertia of a solid regular dodecahedron are equal,…
Q: A 103 kg horizontal platform is a uniform disk of radius 1.71 m and can rotate about the vertical…
A: mass of the uniform disc=103Kg Radius of the disc=1.71 m Moment of inertia of the disc,I=12MR2 (…
Q: A solid cylinder with radius 0.160 mm is mounted on a frictionless, stationary axle that lies along…
A: Given:- R= 0.16 m F= 5 N Slope of θ vs t = m= 16 rad/s2 Analysis: The slope of angular…
Q: small pole (uniform, thin) that has a mass of 4.31 kg and can pivot about an axis perpendicular to…
A:
Q: In a similar problem as before, a 0.443 kg mass hangs from a frictionless pulley with a radius of…
A:
Q: A hoop of mass M = 3.50 kilograms (kg) and radius R = 12.5 centimeters (cm) is resting on a flat…
A:
Q: The string is massless. The pulley turns on frictionless bearings. Consider the pulley as a uniform…
A: Given:-
Q: The kinetic energy of a rotating body is generally written as K=1/2(Iw^2) where I is the moment of…
A: Given that radius is r and mass is m. We are required to find the moment of inertia describe in the…
Q: The length of the bar AP is 750mm. The radius of the pulley is 125mm, Equal forces T-75N are applied…
A:
Q: The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh =…
A:
Q: Question 2: A thin rod of length l has a non-uniform mass distribution as shown in Figure 1. The…
A: Given that: Length of the rod= l Linear mass density, λ=Ax To determine the: Moment of inertia of…
Q: Prove that the moment of inertia of a solid sphere of uniform density, when rotating around a…
A: Let us consider a solid sphere of uniform density rotating about the z-axis. The sphere’s moment of…
Q: M, a solid cylinder (M=1.51 kg, R=0.123 m) pivots on a thin, fixed, frictionless bearing. A string…
A: Given Data:- Mass of the cylinder is M=1.51 kg Radius of the cylinder is R=0.123 m Magnitude of the…
Q: A space station consists of a large, lightweight ring of radius R = 60 m and two small heavy control…
A:
Q: A compound disk of outside diameter 128 CI is made up of a uniform solid disk of radius 44.0 cm and…
A: Total moment of inertia is 10.68kg.m2.
Q: solid cylinder of uniform density
A: Moment of inertia (MI) is the rotational analogue of mass in linear motion. It can be defined with…
Q: Three thin uniform rods each of mass M and length L lie along the x, y, and z axes, with one end of…
A: The masses of the three uniform rods are given as, M1 = M2 = M3 = M The length of the three uniform…
Q: 47, 48, 49, and 50 Assume that the solid has constant density k. 47. Find the moments of inertia for…
A: Given data: Side length of a cube is L Constant density is k
Q: A uniform solid disk has mass M and radius R. A child of mass m = M/2 is standing at two-thirds of…
A: The objective of the question is to find the rotational inertia (moment of inertia) of the system…
Q: uniform solid disk of mass m = 2.95 kg and radius r = 0.200 m rotates about a fixed axis…
A: Given Mass of disk, M = 2.95 kg Radius of disk, R = 0.200 m Angular frequency, w = 5.97 rad/sec
Q: Assume y = 0 + p. Be m A A beam, uniform in mass, M = 27 kg and lengthL = 28 m, hangs by a cable…
A:
Q: A small block of mass mą hangs from a massle with radius of R. The moment of inertia of the Another…
A: GivenI=4 m2 R2m1=2 m2μk=18f=18m1 g
Q: A solid sphere of uniform density has a mass of 2.42 kg and a radius of 0.432 meters. A force of…
A: Given Data: The mass of a solid sphere is, M=2.42 kg The radius of a solid sphere is, R=0.432 m The…
Q: In a similar problem as before, a 0.482 kg mass hangs from a frictionless pulley with a radius of…
A:
Q: Joe's shoulder is labeled S and two points on the cable are labeled P and B. The coordinates of the…
A: The moment of a force depends on the magnitude of the force and the perpendicular distance between…
Q: A hoop of mass M = 3.50 kilograms (kg) and radius R = 12.5 centimeters (cm) is resting on a flat…
A:
Q: Suppose you have a long, thin rod of length 1.51m that is free to rotate about a fixed end. If the…
A:
Q: AF A yoyo is constructed by attaching three uniform, solid disks along their central axes as shown.…
A:
Q: Problem 4 A hoop of mass M = 3.50 kilograms (kg) and radius R = 12.5 centimeters (cm) is resting on…
A: M = 3.5 kg R = 12.5 cm F = 2.75 N I = MR2I = 3.5 * (0.125)2I = 0.0546875 kgm2
Q: The wheels of a wagon can be approximated as the combination of a thin outer hoop of radius rh=0.262…
A:
![A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of
the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the
body.
[Expect to use about half a page to answer the question.]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b7af157-3088-4e07-9322-eb6941ca83f4%2Fb915f503-a6cb-4d36-a5eb-48c8a425c25e%2F11b8f3e_processed.jpeg&w=3840&q=75)
Step by step
Solved in 3 steps with 9 images
- Problem 2: A pulley consists of a large disk of radius R and a small disk of radius r that are welded together and mounted on a horizontal frictionless axle through their common centers. The moment of inertia of this pulley is I. A box containing a turkey of mass M is suspended from a rope wound around the large disk; a box containing a pumpkin of mass m is suspended from a rope wound around the small disk. The ropes do not slip on the disks. The system is released from rest and the turkey begins to descend, while the pumpkin is being lifted up. M P A Derive an expression for the magnitude of the angular acceleration a of the pulley, in terms of system parameters. Assume that a counterclockwise motion of the pulley is the positive direction. MgR+mgR MgR-mgr MgR-mgR a a = a = I+MR2+mr2 I+MR²+mr² I+MR²+mR? MgR+mgr MgR-mgR MgR+mgR a = a = I+MR2+mr²2 I+MR²+mr² I+MR²+mR? Submit I give up! Hint FeedbackA 139-kg platform-oriented horizontally consists of a uniform disk of radius 1.85 m and can rotate about the vertical axis through its center. A 63.3-kg person stands on the platform at a distance of 1.17 m from the center and a 27.5-kg dog sits on the platform near the person, 1.39 m from the center. Find the moment of inertia of this system, consisting of the platform and its population, with respect to the axis.A small block of mass m2 hangs from a massless rope wrapped around a pulley with radius of R. The moment of inertia of the entire pulley is I = 6m2(R)². Another block m1=2m2 is connected to the outer cylinder of the pulley via a horizontal massless rope. The coefficient of kinetic friction between the block and the horizontal surface is µg = 1 (i.e. the frictional force is f = m1g). When m2 is released from rest, what is the angular acceleration a of the block and pulley system? T, m, T. m, Pick the correct answer 最 1 g 18 1 g 10
- A uniform rod of mass 1.90 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.90 kg is attached to one end and a second mass m2 = 3.40 kg is attached to the other end of the rod. Treat the two masses as point particles. (a) What is the moment of inertia of the system? (Answer in kg•m^2) (b) If the rod rotates with an angular speed of 2.60 rad/s, how much kinetic energy does the system have? (Answer in J) (c) Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined? (Answer in kg•m^2) (d) If the rod is of negligible mass, what is the kinetic energy when the angular speed is 2.60 rad/s? (Answer in J)A block of mass mmm = 1.7 kg is attached to a string that is wrapped around the circumference of a wheel of radius RRR = 8.7 cm . The wheel rotates freely about its axis and the string wraps around its circumference without slipping. Initially the wheel rotates with an angular speed ωω, causing the block to rise with a linear speed v = 0.33 m/s. Find the moment of inertia of the wheel if the block rises to a height of h = 7.6 cm before momentarily coming to rest.A uniform rod of mass 2.20 kg and length 2.00 m is capable of rotating about an axis passing through its center and perpendicular to its length. A mass m1 = 4.50 kg is attached to one end and a second mass m2 = 2.60 kg is attached to the other end of the rod. Treat the two masses as point particles.(a)What is the moment of inertia of the system in kg · m2? (b)If the rod rotates with an angular speed of 2.70 rad/s, how much kinetic energy, in joules, does the system have? (c)Now consider the rod to be of negligible mass. What is the moment of inertia of the rod and masses combined, in kg · m2? (d)If the rod is of negligible mass, what is the kinetic energy, in joules, when the angular speed is 2.70 rad/s?