Three thin uniform rods each of mass M and length L lie along the x, y, and z axes, with one end of each at the origin. Given I = 1/12 ML2 for a rod pivoted about its center of mass, find I about the z-axis for the three-rod
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Three thin uniform rods each of mass M and length L lie along the x, y, and z axes, with one end of each at the origin. Given I = 1/12 ML2 for a rod pivoted about its center of mass, find I about the z-axis for the three-rod
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- A stick is resting on a concrete step with of its total length L hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest at 0= 62.1° with respect to the horizontal, as shown in the figure. If the mass of each bug is 2.92 times the mass of the stick and the stick is 10.3 cm long, what is the magnitude a of the angular acceleration of the stick at the instant shown? Use 8 = 9.81 m/s². α = 28.21 rad/s² Figure is not to scale. 0A stick is resting on a concrete step with of its total length L hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest at 0= 56.9° with respect to the horizontal, as shown in the figure. If the mass of each bug is 2.75 times the mass of the stick and the stick is 11.5 cm long, what is the magnitude a of the angular acceleration of the stick at the instant shown? Use g = 9.81 m/s². α = 4.45 Incorrect rad/s² L Figure is not to scale.Two astronauts, each having a mass of 75.5 kg, are connected by a 10.0 m rope of negligible mass. They are isolated in space, moving in circles around the point halfway between them at a speed of 4.90 m/s. Treating the astronauts as particles, calculate each of the following. Center of gravity (a) the magnitude of the angular momentum of the system kg-m²/s (b) the rotational energy of the system KJ By pulling on the rope, the astronauts shorten the distance between them to 5.00 m. (c) What is the new angular momentum of the system? kg-m²/s (d) What are their new speeds? m/s (e) What is the new rotational energy of the system? KJ (f) How much work is done by the astronauts in shortening the rope? kJ
- Problem 3: Suppose we want to calculate the moment of inertia of a 65.5 kg skater, relative to a vertical axis through their center of mass. Part (a) First calculate the moment of inertia (in kg m2) when the skater has their arms pulled inward by assuming they are cylinder of radius 0.11 m. sin() cos() tan() 7 8 9 HOME cotan() asin() acos() E 4 5 atan() acotan() sinh() 1 3 cosh() tanh() cotanh() END ODegrees O Radians Vol BACKSPACE DEL CLEAR Submit Hint Feedback I give up! Part (b) Now calculate the moment of inertia of the skater (in kg m?) with their arms extended by assuming that each arm is 5% of the mass of their body. Assume the body is a cylinder of the same size, and the arms are 0.825 m long rods extending straight out from the center of their body being rotated at the ends.Please help meof Sides a and b has a mass M. Four point-like balls, each of rnass m = each corner of the plate as indicated in the figure. What is the moment of inertia of this object if the axis of M are glued to rotation is through the end of one sidt, like a door, as indicated in the figure by the blue fine? (A) Isoor=M (a² + b²) (B) Isoor= M(a² + b) (C) Idoor M(a² + b*) (D) Isoor = }M(a²+8) (F) Isoor = Ma² %3D (G) Isoor Ma? %3D (H) Idor Ma² A rectangular plate with four umall point-like balls glued to each corner. The blue line represents the axis of rotation
- On average, both arms and hands together account for 13% of a person's mass, while the head is 7.0% and the trunk and legs account for 80%. We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 67.0 kg skater is 1.60 m tall, has arms that are each 64.0 cm long (including the hands), and a trunk that can be modeled as being 32.0 cm in diameter. If the skater is initially spinning at 64.0 rpm with her arms outstretched, what will her angular velocity @2 be (in rpm) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble. W2 = rpm Question Source: FreedA 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?A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.99 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. |kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim? |kg · m2/s
- In the figure here, three particles of mass m = 0.017 kg are fastened to three rods of length d = 0.15 m and negligible mass. The rigid assembly rotates about point O at angular speed w = 0.55 rad/s. About O, what are (a) the rotational inertia of the assembly, (b) the magnitude of the angular momentum of the middle particle, and (c) the magnitude of the angular momentum of the assembly? M (a) /= i (b) L₂ = i (c) Ltot 0 mA stick is resting on a concrete step with of its total length L hanging over the edge. A single ladybug lands on the end of the stick hanging over the edge, and the stick begins to tip. A moment later, a second, identical ladybug lands on the other end of the stick, which results in the stick coming momentarily to rest at 0 = 36.1° with respect to the horizontal, as shown in the figure. If the mass of each bug is 2.75 times the mass of the stick and the stick is 15.1 cm long, what is the magnitude o of the angular acceleration of the stick at the instant shown? Use g = 9.81 m/s². α = 8.4 Incorrect rad/s² L Figure is not to scale. 0A 7.33 kg particle with velocity (1.80 m/s)i (6.97 m/s ) is at x = 5.08 m, y = 3.64 m. It is pulled by a 5.87 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 i (b) Number (c) Number I i = k Units k Units k Units >