Review. A conical pendulum consists ofa bob of mass m in motion in a circularpath in a horizontal plane as shown inFigure Pl1.12. During the motion, the sup-porting wire of length { maintains a con-stant angle 0 with the vertical. Show thatthe magnitude of the angular momentum10of the bob about the vertical dashed line ism²ge% sin* e\1/2L =Figure P11.12Cos e

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Answered: Review. A conical pendulum consists of…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter13: Rotation Ii: A Conservation Approach

Section: Chapter Questions

Problem 47PQ

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A thin rod of length 2.65 m and mass 13.7 kg is rotated at anangular speed of 3.89 rad/s around an axis perpendicular to therod and through one of its ends. Find the magnitude of the rodsangular momentum.
A 1.91 kg particle-like object moves in a plane with velocity components vx = 78.6 m/s and vy = 91.3 m/s as it passes through the point with (x, y) coordinates of (1.15, -2.20) m. Just then, in unit-vector notation, what is its angular momentum relative to (a) the origin and (b) the point (-1.20, -1.20) m?
A particle is to move in an xy plane, clockwise around the origin as seen from the positive side of the z axis. In unit-vector notation, what torque acts on the particle if the magnitude of its angular momentum about the origin is (a) 4.0 kgm2/s, (b) 4.0t2 kgm2/s, (c) 4.02t kgm2/s, and (d) 4.0/t2 kg m2/s?
The homogeneous, solid cylinder with mass m = 4.7 kg and radius r = 0.56 m rolls along the inclined surface without slipping. If the initial angular velocity is ω1 = 2.6 rad/s (counterclockwise), and after a certain time lapse the angular velocity is ω2 = 2.8 rad/s (clockwise), determine the magnitude of the component of the linear impulse parallel to the inclined surface due to gravitational force during this time period. Let θ = 65o. Choose the correct answer: a) 20.71 N.s b) 11.94 N.s c) 7.106 N.s d) 19.49 N.s e) 21.32 N.s
Modeled after the triatomic molecule problem that is let's consider the three atoms composing the molecule have different masses and coordinate, while the axis of rotation is still y-axis. The first atom has a mass of 6.778 kg, with x coordinate at 2.814 m and y coordinate at 9.967 m. The second atom has a mass of 48.003 kg, with x coordinate at 47.145 m and y coordinate at 17.003 m. The third atom has a mass of 43.312 kg, with x coordinate at 44.89 m and y coordinate at 22.657 m. What is the moment of inertia in the unit of kg m2 with respect to the y axis?
A figure skater rotating at 3.4 rad/s with arms extended has a moment of inertia of 2.97 kg ∙ m2. If he pulls in his arms so his moment of inertia decreases to 1.9 kg ∙ m2, what is the final Kenetic energy?
A 2.0 kg particle is traveling clockwise in a circular path with a radius of 1.0 m with a velocity 5.0 m/s. What is the angular momentum of the particle about the origin? (i is the unit vector in the direction of the +x axis, j is the unit vector in the direction of the +y axis, k is the unit vector in the direction of the +z axis)
A light rod of length l= 1.00 mrotates about an axis perpendicularto its length and passingthrough its center as inFigure P8.51. Two particles ofmasses m1 = 4.00 kg and m2 =3.00 kg are connected to theends of the rod. (a) Neglectingthe mass of the rod, what is thesystem’s kinetic energy whenits angular speed is 2.50 rad/s?(b) Repeat the problem, assumingthe mass of the rod is takento be 2.00 kg.
Prove that the moment of inertia of a solid cylinder of uniform density, when rotating around its central axis,is MR2/2, where M is the mass of the cylinder and R is its radius. Hint: integrate the infinitesimal volume element in cylindrical coordinates
On a frictionless table, a m = 0.70kg glob of clay strikes a uniform M = 0.82kg bar perpendicularly at a point b = 0.49m from the center of the bar and sticks toit. The bar is L = 1.22 m long and the clayis moving at v = 5.50 m/s before strikingthe bar.At what angular speed does the bar/claysystem rotate about its center of mass after the impact? ote: correct answer should be: Xcm(center mass after the impact =0.68m Angular velocity=mv(0.42)/(1/12Ml^2+m(0.42)^2+0.07^2M, I'd like to know the reason why need add the 0.07^2M Part
A 5.00 kg disk of radius 1.20 m initially rotated at 2.00 rad/s relative to a fixed axis passing through its center of mass. Then 3.00 J of work is then added to the system. What will be the final kinetic energy of the disk? The moment of inertia of a disk of mass M and radius R is 1/2 MR^2.
On a frictionless table, a m = 0.70kg glob of clay strikes a uniform M = 0.82kg bar perpendicularly at a point b = 0.49m from the center of the bar and sticks toit. The bar is L = 1.22 m long and the clayis moving at v = 5.50 m/s before strikingthe bar.What is the final speed of the center ofmass?At what angular speed does the bar/claysystem rotate about its center of mass after the impact?

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