Question 4: An annulus of inner and outer radii Rị and R2 has a non-uniform surface mass density given by o = 0or where o is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 2. a) Find the moment of inertia of the rod about an axis passing through its center of mass (the origin). Express your result in terms of M (mass of the annulus) and R1 and R2. b) Check your result as R1 - 0 and R2 = R.

Question 4: An annulus of inner and outer radii Rị and R2 has a non-uniform surface mass density given by o = 0or where o is a positive constant and r is the radial distance from the origin (radial coordinate in the cylindrical coordinates) as shown in Figure 2. a) Find the moment of inertia of the rod about an axis passing through its center of mass (the origin). Express your result in terms of M (mass of the annulus) and R1 and R2. b) Check your result as R1 - 0 and R2 = R.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Similar questions

Problem 2: A physical pendulum consists of a disk of radius R and mass 2m fixed at the end of a rod of mass 3m and length 4R as shown in the figure below. Please express your answers in terms of the given quantities and fundamental constants. 3m 4R R 2m a. Determine an expression for the position of the center of mass of the apparatus (relative to the upper end of the rod). Answer 2a:
A thin rod of length 2.6 meters has a non-uniform density given by ρρ = b(x2 + ax) where b = 1.18 kg/m3, a = 0.32 m, and x measures from one of the rod to the other. Find the rod's center of mass.
A member is loaded with force system as shown in figure. Find the Moment about A, B, C, D and E Where F1= 70 N, F2 =30 N, F3 =10 N, F4 =40 N, F5 =50 N, AB =110 m, Point C is in the mid of AE, CD = 50m, AE =150 m. the angle 8 =25° (5 marks) (Enter only the values in the boxes provided) F4 F1 F3 B F2 (i) The moment about the point 'A' (unit in Nm), MA = (ii) The moment about the point 'B' (unit in Nm) ,MB = (iii) The moment about the point 'C' (unit in Nm), Mc = (iv) The moment about the point 'D' (unit in Nm) , Mp = (v) The moment about the point 'E'(unit in Nm) , MẸ =
A 230-kg, 2.70-m long beam slides across the ice with a speed of 18.0 m / s (see figure). A 65.0-kg man at rest grasps it by one end (without lifting) and holds onto it; both he and the beam begin to spin on the ice. Assume frictionless motion. (a) How fast is the center of mass of the system moving after the collision? (b) With what angular speed does the man-beam system rotate with respect to its Center of Mass?
A solid sphere of mass, M = 5.0 kg, and radius, R = 0.100 m is placed on two blocks so that it’s centre of mass lies at the origin as shown on the right. A bullet of mass, m = 0.100 kg, and with an x coordinate of b = 0.04 m strikes the sphere from below with a vertical velocity, v = 65 m/s and embeds in the sphere coming to rest at the location (-b,0) in the diagram below. Since there is no momentum in the horizontal direction, after the bullet hits the sphere , it will rise up to some maximum height and then fall back to its initial position on the two blocks. While the sphere is in the air it will rotate. What is the magnitude of the angle (in degrees) through which the sphere will rotate before it makes contact with the two blocks again?
(b) Two spheres, each of mass m, are connected by a rod. (The mass of the rod is so small that it can be ignored.) The X shows the position of the center of mass (cm) of the system. Three possible Mass m Mass m rotation axes, 1, 2, and 3, are shown. Rank the moments of inertia of cm the system for these three axes, from largest to smallest. Explain how you made your ranking. Axis Axis Axis # 1 #2 # 3 (c) Two spheres, one of mass m and one of mass 2m, are connected by a rod. (The mass of the rod is so small that it can be ignored.) The X shows the position of the center of mass (cm) of the system. Three Mass m Mass 2m possible rotation axes, 1, 2, and 3, are shown. Rank the moments of |cm inertia of the system for these three axes, from largest to smallest. Explain how you made your ranking. Аxis # 1 Аxis Axis # 3 # 2
A uniform rod of lenght L=20 cm and mass M-1 kg is lying on a frictionless table. You slide a small piece of putty of mass m=100 gr across the table so that it hits the rod straight on 5 cm from the end with a velocity v=10 m/s. After the collission the putty sticks to the rod. 1. What is the velocity of the centre of mass for the putty+rod system. 2. Where is the centre of mass of the putty+rod system 3. What is the angular speed of the putty+rod system around the centre of mass 4. What is the change in energy after the collission?
Course dashboard Q: A uniform semicircular plate of thickness d and radius R is pivoted about an axis perpendicular to the plate and passing through its center. How far from the center is the CM located? C E A R/2 R/3 2R/3 R/6 2R Lütfen birini seçin O A
The 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.
contine the other three d,e,f
Can you please help me solve this.. Three masses A = 3kg , B = 4kg and C = 5kg are connected by rods of negligible mass to form an equilateral triangle of side 8m as shown. Determine the individual moment of inertia and total moment of inertia of the system about axis XY. Solve for: (a) Total moment of inertia of the system (b) Moment of inertia of object C (in kg-m^2) (c) Moment of inertia of object B (in kg-m^2) (d) Moment of inertia of object A (in kg-m^2) •Pls answer with complete and detailed solution (3 DECIMAL PLACES all final answers with correct units) •Sketch an illustration/diagram with labels (this is a must; for a better understanding) Thank you I will give your answer a LIKE for helping me...
A 4.00-kg mass and a 3.00-kg mass are attached to opposite ends of a thin 39.2 cm-long horizontal rod (see the figure (Figure 1)). The system is rotating at angular speed w = 6.00 rad/s about a vertical axle at the center of the rod. v Correct Part C Determine the kinetic energy K of the system assuming that the axle passes through the CM of the system. να ΑΣφ K = J Submit Previous Answers Request Answer Figure 1 of 1 X Incorrect; Try Again; 5 attempts remaining 3.00 kg Part D 4,00 kg Determine the net force on each mass assuming that the axle passes through the CM of the system Enter your answers numerically separated by a comma. Masaūstü Aramak için buraya yazın delete prt sc esc 14 f5 16 f7 19 13) & 5 /2 8 1 3 23 6 7 13+