From a circular disc of radius R and mass 9M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is (2005) (a) 4MR² (c) 10MR² (b) (d) 40 9 37 9 MR² -MR² R/3 R
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- i need the answer quicklyA yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M, radius R, and moment of inertia 1/2MR2. The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F. The coefficient of friction between the yoyo and the tabletop is μ. The tension in the string is not sufficient to cause the yoyo to leave the tabletop.a. Develop an expression for the moment of inertia ICM about the central axis of the yoyo in terms of the given quantities and fundamental constants. ICM = b. Determine an expression for the magnitude of the torque τ exerted by the string about the contact point of the yo-yo with the table. τ =c. Develop an expression for the moment of inertia of the yo-yo…A particle of mass m = 10 kg is rotating around a point O at a radius r = 10 m. The angular position of the particle is given by θ(t) = (1/2)*t^3 − 5t^2 + t. What is the torque on the object at t = 3 s?
- Four particles with masses 7 kg, 2 kg, 7 kg, and 4 kg are connected by rigid rods of neg- ligible mass as shown. Aassume the system. rotates in the xy plane about the z axis (ori- gin, O) with an angular speed of 6 rad/s. 7 kg y A 4 kg 2 kg 6 rad/s 7 kg Т 5 m Find the moment of inertia of the system about the z axis. Answer in units of kg. m². Your response... Previous Responses X #1.490 PALETTEA merry-go-round rotates at the rate of 0.20 rev/s with an 75 kg man standing at a point 2.0 m from the axis of rotation. (a) What is the new angular speed when the man walks to a point 0.6 m from the center? Assume that the merry-go-round is a solid 25 kg cylinder of radius 2.0 m. 5.71 v rad/sec (b) Calculate the change in kinetic energy due to this movement. X JFrom a solid sphere of mass M and radius R, a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is MR² (b) 32 √2π (a) 4MR² 9√3π (c) MR² 16 √2 G4MR² (d) 3√3π polit
- The end state of our sun will most likely be a white dwarf star. It would have about one fourth of its current mass and a radius about two percent of its current radius. The Sun today takes 30 days to rotate once about its internal spin axis. This is equivalent to an angular speed of 2.42 x 10-6 rad/s. Its moment of inertia today can be approximated as 3.86 x 1047 kg m². Its final angular speed will be 2.42 x 10-2 rad/s. What would its' final moment of inertia be? Select one: a. b. 1.52 x 10-55 kg m² OC. 6.59 x 1054 kg m² 3.86 x 1051 kg m² 3.86 x 1043 kg m² d.59. ssm Two disks are rotating about the same axis. Disk A has a moment of inertia of 3.4 kg · m² and an angular velocity of +7.2 rad/s. Disk B is rotating with an angular velocity of -9.8 rad/s. The two disks are then linked together without the aid of any external torques, so that they rotate as a single unit with an angular velocity of –2.4 rad/s. The axis of rotation for this unit is the same as that for the separate disks. What is the moment of inertia of disk B?In the figure, three 0.10 kg particles have been glued to a rod of length L = 11 cm and negligible mass and can rotate around a perpendicular axis through point O at one end. How much work is required to change the rotational rate (a) from 0 to 20.0 rad/s, (b) from 20.0 rad/s to 40.0 rad/s, and (c) from 40.0 rad/s to 60.0 rad/s? (d) What is the slope of a plot of the assembly's kinetic energy (in joules) versus the square of its rotation rate (in radians-squared per second-squared)? Axis -P--P-- P- (a) Number i Units (b) Number i Units (c) Number i Units (d) Number i Units
- A circular cone with constant density 1, base radius 6, and height 8 is placed so the axis of symmetry is on the z-axis. A cylindrical hole of radius 1 is drilled through the axis of symmetry. Find the moment of inertia of the remaining shape. (The moment of inertia about the z-axis will be the same no matter where the shape is placed along the z- axis and whether the shape is pointing up or pointing down.)A sphere of radius r is undergoing pure rolling with constant angular velocity on a fixed curved surface of radius R with O as centre as shown. The ratio of the angle through which line PC rotates to the angle through which line OC rotates is : 3. R+r R-r R+r R-r (A) r (B) r (C) R (D) RQuestion 5 only.......