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A DVD of mass M = 20.0 g = 0.0200 kg and radius R = 6.00 cm = 0.0600 m is rotating freely around a fixed vertical axis without any friction. Its initial angular velocity is ?1= 102 rad/s. A bug of mass m = 6.00 g = 0.00600 kgdrops onto the center of the rotating DVD. The bug then walks radially outward toward the edge of the DVD without slipping until it reaches a distance r from the center,...
A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass. The axis is perpendicular to the disk. The moment of inertial for the disk with a central axis is I MR2. Two non-rotating smaller disks, each with mass M2 and radius R/4, are glued on the original disk as shown in the figure. (a) Show that the ratio of the moments of inertia is given by I'/I = 35/16, where I' is the moment...
A disc of moment of inertia 3.00 kgm2 is rotating with angular velocity 2.00 rad/s about an axis perpendicular to its plane and passing through its centre. Another disk (which is not rotating) of moment of inertia 5.00 kgm2 is gently placed over it. Finally, the two discs rotate with the same angular velocity around the common rotational axis. The new angular velocity of the combined disc (in rad/s) is ?
Question 1. A uniform circular disc of mass m and radius r is pivoted at point 0, as shown in Figure 1. The disc is released from the position shown. Immediately after the release: (a) Obtain the angular acceleration of the disc in terms of r,1,g, and 0. [5 marks) [8 marks) Assuming r = 0.5 m and @ = 30° and using plot function in MATLAB: (b) Determine how the initial angular acceleration changes as I is varried from...
A gramophone record consists of a uniform circular disk of radius R and total mass M with a hole punched through it's center with a radius r. a) Show that the moment of inertia of the record about the perpendicular axis passing through it's center is 1/2 M(R^2 + r^2). b)A gramophone record having a mass of m=100g, radius =15cm and hole of radius 3cm is rotating freely on a turntable at 33 revolutions per minute with no friction. A...
A flat horizontal disc of moment of inertia 2.2 kg m2 is rotating at 4.5 rad s-1 about a vertical axis through its centre. A 0.13 kg mass is dropped onto the disc, landing without slipping 1.4 m from the centre. Calculate the new angular velocity of the disc, in rad s-1 , to 2d.p.
A thin uniform rod has a length of 0.530 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.41 rad/s and a moment of inertia about the axis of 3.10×10−3 kg⋅m2 . A bug initially standing on the rod at the axis of rotation decides to crawl out to the other end of...
A thin uniform rod has a length of 0.520 m and is rotating in a circle on a frictionless table. The axis of rotation is perpendicular to the length of the rod at one end and is stationary. The rod has an angular velocity of 0.37 rad/s and a moment of inertia about the axis of 2.70×10−3 kg⋅m2 . A bug initially standing on the rod at the axis of rotation decides to crawl out to the other end of...
A disc as moment of inertia 4 kg · m² and a radius of 1.43 m revolves around a fixed, frictionless axis perpendicular to the disc and passing through the center of the disc. A force of 15 N is applied tangentially to the edge of the disc, which starts from the rest. Determine the angular velocity after the disk completes 2.7 revolution (s). Choose one: a)ω = 2.5 rad / s b)ω = 9.4 rad / s c)ω =...
10. A body rotating at the angular speed of 20 rad/s slows down to an angular spee seconds. What is the average angular acceleration? 11. A body is rotating with an angular acceleration of 2 rad/s What is the linear acceleration of a point in this body that is 2.1 m from the axis of rotation? 12. Two masses, each of mass M, are separated by a distance D. a) what is the moment of inertia, if the axis of...