Find the moment of inertia of a rectangular sheet of metal of sides a and b with respect to side a. Express the result in terms of the mass of the metal sheet, m.
Q: A uniform steel rod of length 0.6 m and mass 1.6 kg has two point masses on each end. The point mass…
A: Introduction: Given data: Length of the rod is, L=0.6 m Mass of the rod is, M= 1.6 kg The point mass…
Q: A 133 kg horizontal platform is a uniform disk of radius 1.79 m and can rotate about the vertical…
A: Given:mass of the disk, m = 133 kgradius of the disk, r = 1.79 mmass of the person, mp = 61.7…
Q: A uniform rectangular block has mass M and sides 2a, 2b and 2c. Find the principal moments of…
A:
Q: A spacecraft is in empty space. It carries on board a gyroscope which is a device that changes the…
A: using equation of motion w2 = wo2 + 2α∆θwhere w is the final angular velocity wo is the initial…
Q: The tension in the cable from D to A is 75 N. Determine the moment of this force about point O…
A: TAD = 75 N
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 rugby player is pivoting about his longitudinal axis and his moment of inertia about this axis is…
A:
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: Along the length of a rod, the linear mass density of the rod is λ(x)=2.1x-x2/5.2, where L = 1 m is…
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: 129-kg horizontal platform is a uniform disk of radius 1.61 m and can rotate about the vertical axis…
A:
Q: A solid sphere of mass M = 2.95 kg is mounted on a frictionless axle, which goes through its center.…
A:
Q: our objects are held in position at the corners of a rectangle by light rods. m1 (kg) m2 (kg) m3…
A: Given:- Four objects are held in position at the corners of a rectangle by light rods. m1 (kg) m2…
Q: A hollow, thin-walled sphere of mass 12.0 kg and diameter 48.0 cm is rotating about an axle through…
A: This problem can be solved using concept of angular momentum.
Q: Four identical spheres of masses 2.0 kg each and radius 0.25 m are situated at the four corners of a…
A: Given: m=2.0kgradius,r=0.25m To find: Moment of inertiaa)passing through centre of the…
Q: A particle is acted on by two torques about the origin: t1 has magnitude of 2.0 Nm and is directed…
A:
Q: The position vector of a 2.5 kg particle is given by r = 4.0 î +3.0 t ĵ, where r is in meters and t…
A: This problem can be solved using basic mathematical expressions for given physical quantities.
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: uniform rod of mass 3.4 kg is 4 m long. The rod is pivoted about a horizontal, frictionless pin at…
A: Given,Mass of the rod, m = 3.4 kglength of the rod, l = 4 mθ = 70°acceleration due to gravity, g =…
Q: A 101 kg horizontal platform is a uniform disk of radius 1.61 m and can rotate about the vertical…
A: Given Mass of horizontal platform = 101 kg (uniform disk ) Radius of platform = 1.61 m Mass of a…
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: 119 kg horizontal platform is a uniform disk of a radius of 1.97 m and can rotate about the vertical…
A: Moment of inertia of this system is given as I=Idisk +Idog+Iperson We know that Idisk=0.5M1R12…
Q: A 1.50 kg mass moves in the x and y plane according to vector r = (6t^3+t)i+ (15t^2 + 3)j (relative…
A:
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: time t = 0. Relative to an x-y coordinate system, where upward is the positive y direction and the x…
A:
Q: The member shown below is fixed at O and its dimensions are h1h1 = 1.10 mm, h2h2 = 0.20 mm, and ww =…
A:
Q: Treat the upper limb as one segment with a centre of mass (d2) 36.0 cm from the shoulder joint. The…
A: The objective of this question is to determine the vertical component of the force created by the…
Q: Two spheres each with a radius of 5.0 cm and mass of 0.50 kg are free to slide along a thin rod with…
A: Let I0 and I denote the initial and final moments of inertia of the given structure. Let ω0 and ω…
Q: In a similar problem as before, a 0.482 kg mass hangs from a frictionless pulley with a radius of…
A:
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
- A hoop of mass M = 3.50 kilograms (kg) and radius R = 12.5 centimeters (cm) is resting on a flat surface. There is a constant, horizontal force with a magnitude F = 2.75 Newtons (N) acting at the center of mass of the hoop. As a result, the hoop begins to roll without slipping. The moment of inertia of a hoop is given by I = MR2. Find the resulting linear acceleration of the hoop, in units of meters per second squared (m/s2). CM X- FTake an equilateral triangular sheet of side, and remove the "middle" triangle (1/4 of the area). Then remove the "middle" triangle from each of the remaining three triangles, and so on, forever. Let the final object have mass. The moment of inertia of final object about axis passing through 'O' and perpendicular to plane of object is ml²/x. Then the value of x isA 117 kg horizontal platform is a uniform disk of radius 1.67 m and can rotate about the vertical axis through its center. A 62.7 kg person stands on the platform at a distance of 1.11 m from the center, and a 29.5 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. moment of inertia: kg · m?
- ssa In unit-vector notation, what is the torque about the origin on a particle located at coordinates (0, -4.30 m, 3.14 m) due to (a) force F with components Fx= 3.18 N and F1y= F1z= 0, and (b) force F 2 with components F2x = 0, F2y = 4.53 N, F22 = 5.74 N? (a) Number i k Units (b) Number i k Units eTextbook and Media Save for Later Attempts: 0 of 8 used Submit Answer Qu Friday tv DII 80 888 esc FB F9 F4 F5 F6 F7 F2 F3Two kids, each with a mass of 25.0 kg, are standing at the edge of a merry-go-round. Treat both kids as point masses. The merry-go-round is a uniform disk with a mass of 97.5 kg and a radius of 1.25 meters, which is free to rotate about its center of mass without friction. The moment of inertia of a solid disk rotating about its center of mass is given by I = MR2 /2 , and the moment of inertia of a point mass is given by I = mr2 . The merry go round is initially rotating at 12.5 revolutions per minute (rpm). a) If both kids walk to the center of the merry-go-round, what will the final angular speed be, in rpm? Hint: use conservation of angular momentum. b) What is the change in the total kinetic energy of the disk and the two kids during this process? Give your answer in units of Joules (J)A hoop of mass M = 3.50 kilograms (kg) and radius R = 12.5 centimeters (cm) is resting on a flat surface. There is a constant, horizontal force with a magnitude F = 2.75 Newtons (N) acting at the center of mass of the hoop. As a result, the hoop begins to roll without slipping. The moment of inertia of a hoop is given by I = MR2. Find the resulting linear acceleration of the hoop, in units of meters per second squared (m/s2).
- John McClane, desperately trying to escape the bad guys in an upper floor of a skyscraper, grabs a fire hose and crashes out a window. He falls toward the ground, dragging the hose with him. The hose is wound around a cylinder that has a moment of inertia equal to 5 kg m2, and the hose unspools from the cylinder as McClane falls. Assuming that the hose is pulled from the cylinder at an angle that is perpendicular to the cylinder's radius, what is McClane's acceleration? Let McClane's mass be 75 kg and the radius of the cylinder be 0.5 m. Neglect friction and air resistance. Hose Wall Spool McClaneThe moment of inertia for a set of objects of mass m; rotating about a common axis is defined as 1 = Σm₁r? 2 where r, is the distance of the ith object to the axis of rotation. If there are many particles that make up a larger object then this sum transforms into an integral, 4-fff or a. I = dV, V where p is the mass density and V the volume of the object. In this exercise we will explore moment of inertia by rolling two objects down an incline plane in the Experimental Math Lab Space.A 8.44 kg particle with velocity 8.68 m/s 1.17 m/s is at x = 7.12 m, y = 9.61 m. It is pulled by a 8.42 N force in the negative x direction. About the origin, what are (a) the particle's angular momentum, (b) the torque acting on the particle, and (c) the rate at which the angular momentum is changing? (a) Number Units (b) Number Units (c) Number Units 111
- A 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.Four small spheres, each of which you can regard as a point of mass 0.200 kgkg, are arranged in a square 0.400 mm on a side and connected by light rods. Find the moment of inertia of the system about an axis through the center of the square, perpendicular to its plane. Find the moment of inertia of the system about an axis bisecting two opposite sides of the square. Find the moment of inertia of the system about an axis that passes through the centers of the upper left and lower right spheres and through point O.A child's top is held in place upright on a frictionless surface. The axle has a radius of r 3.21 mm. Two strings are wrapped around the axle, and the top is set spinning by T T applying T = 2.40 N of constant tension to each string. If it takes 0.590 s for the string to unwind, how much angular 2r momentum L does the top acquire? Assume that the strings do not slip as the tension is applied. R SP 9.15 x10¬3 kg-m² L = S Point P is located on the outer surface of the top, a distance h = 35.0 mm above the ground. The angle that the outer surface of the top makes with the rotation axis of the top is 0 = 24.0°. If the final tangential speed v, of point P is 1.45 m/s, what is the top's moment of inertia I? T 2r T 2.42 x10-4 kg-m? = Incorrect