Rotational kinetic energy is yet another mass-dependent engineering quantity. An object having a mass moment of inertia I and rotating with angular speed of ω (rad/s) has a rotational kinetic energy which is equal to 1/2 I ω2 . Determine the rotational kinetic energy of a steel shaft that is 2 m long and has diameter of 5 cm and is rotating at an angular speed of 100 rpm.

Q: A solid cylinder has a mass 2.45kg and a radius 0.746 m. What is its moment of inertia (in unit of…

A: The formula for the moment of inertia when a solid cylinder is rotating about its central axis is:

Q: In the figure, a constant horizontal force F→app of magnitude 6.5 N is applied to a wheel of mass…

A: Given data;Horizontal force, Fapp = 6.5 NMass of the wheel. m = 6.1 kgRadius of the wheel, R = 0.52…

Q: A 40-kg cylinder pulley with a radius of 0.2 m rotates at a constant angular speed of 4 rad/s. What…

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Q: translational kinetic energy, and what fraction of the kinetic energy is rotational kinetic energy?…

A: m = 2.4 kg r = 0.62 m w = 58 rpm

Q: Problem 9: The rotational inertia of a collapsing spinning star drops from an initial value I= 9 x…

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Q: A solid, horizontal cylinder of mass 14.0 kg and radius 1.00 m rotates with an angular speed of 6.00…

A: Moment of inertia of cylinder and putty -  Icylinder=12MR2Iputty=mr2 Angular momentum…

Q: In the figure, two particles, each with mass m = 0.80 kg, are fastened to each other, and to a…

A: mass of particles , m = 0.8 kg mass of rod , M = 1.1 kg Angular speed , ω = 0.34 rad/s d = 5.4 cm =…

Q: In the figure here, three particles of mass m = 0.017 kg are fastened to three rods of length d=…

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Q: A thin stickof mass m=0.2 kg and length L= 4.6 m, is attached to the rim of a metal disk of mass…

A: The rotational inertia around the axis of rotation is given by using the theorem of the parallel…

Q: A ring of mass 0.2 kg is placed at the top of an inclined plane with angle 0 = 30°. The ring has…

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Q: The specifications for a ceiling fan you have just bought indicate that the total moment of inertia…

A: (a) The equation for the angular acceleration is given by, α=τI Here, τ is the torque and I is the…

Q: A 2.0-kg solid cylinder 1radius = 0.10 m, length = 0.50 m2 isreleased from rest at the top of a ramp…

A: Given, Mass of the cylinder, m = 2.0-kg The radius of the cylinder, r = 0.10 m The length of the…

Q: Two uniform solid cylinders, each rotating about its central (longitudinal) axis, have the same mass…

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Q: When a solid sphere is rotating at a constant angular w = 2.5 rad/s, what is the rotational kinetic…

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Q: The assembly shown in the figure below consists of a thin rod of length e = 23.2 cm and mass m =…

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Q: a rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four…

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Q: A thin stick of mass M3D0.2 kg and length L=4.0 m, is attached to the rim of a metal disk of mass…

A: Given, Mass of disc,m1=2 kg Mass of stick,m2=0.2 kg Length of stick,L=4 m Radius of disc,R=0.4 m

Q: 13. Rigid rods of negligible mass lying along the y-axis connect three particles. The system rotates…

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Q: In the figure, two particles, each with mass m = 0.78 kg, are fastened to each other, and to a…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: disk-shaped motor component is running with angular velocity ω0=16.26 rad/s around its axis of…

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Q: The uniform rod (length 0.573 m) in the figure rotates in the plane of the figure about an axis…

A: Rotational Inertia= Irod=0.362 kg. m2 Angular speed(ωrod)=3.34 rad/s' Length of the rod (r)=0.573 m…

Q: A thick cylinder of inner radius 10 cm and outer radius 50 cm rolls at 4 m/s without slipping. If…

A: Given data The cylinder's inner radius is: r = 10 cm = 0.1 m The outer radius of the cylinder is: R…

Q: The uniform rod (length 0.60 m, mass 1.0 kg) rotates in the plane of the figure about an axis…

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Q: A hollow sphere has a mass of 15 kg, an inner radius of 12 cm and an outer radius of 18 cm. What is…

A: To find out the rotation inertia of the sphere passing through its centre.

Q: Suppose you have a long, thin rod of length 1.31m that is free to rotate about a fixed end.  If the…

A: Given in question: Length of rod(L) = 1.31 meters                                  Mass of rod(M) =…

Q: The assembly shown in the figure below consists of a thin rod of length { = 22.2 cm and mass m =…

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Q: In the figure. two particles. each with mass m 0.95 kg. are fastened to each other, and to a…

A: Given,mass of the each particle, m = 0.95 kglength of the rod, d = 5.8 cmmass of the rod, M = 1.0…

Q: Two uniform solid cylinders, each rotating about its central (longitudinal) axis, have the same mass…

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Q: The figure shows three 0.0147 kg particles that have been glued to a rod of length L=6.01 cm and…

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Q: A flywheel is a mechanical device used to store rotational kinetic energy for later use. Consider a…

A: Given information: Here, m1 and m2 are the mass of the first and the second flywheel respectively,…

Q: force F→app of magnitude 11 N is applied to a wheel of mass 11 kg and radius 0.19 m. The wheel rolls…

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Q: What must be the radius (in cm) of a disk of mass 17 kg, so that it has the same rotational inertia…

A: Given data: Mass of disk, md=17 kg Mass of sphere, ms=4 g =4×10-3 kg Radius of sphere, rs=3 m Our…

Q: A solid disk with rotational moment of inertia of 15.5 kg m2 starts from rest and accelerates under…

A: Given: M.I of solid disk→Is=15.5 kg m2 Torque→τ=8.72 N m Time interval →t=4.31 s Let's find disk's…

Q: you double the diameter of a wheel and hold all other physical characteristics of the wheel…

A: The wheel is supposed to be a ring Moment of inertia or ring = MR2

Q: A disc of radius R = 2 m has a moment of inertia | = 250 kg.m2 and is rotating at 10 rev/min about a…

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Q: In the figure, two particles, each with mass m = 0.78 kg, are fastened to each other, and to a…

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Q: A 2.00 kg solid, uniform sphere rolls without slipping across a level surface, translating at 4.00…

A: Transnational KE is 16 J

Q: A wheel, with rotational inertia I, mounted on a vertical shaft with negligible rotational inertia,…

A: Answer :- (a) 12.40 rad/s Given  Initial angular speed (wi) = 37.2 rad/s  Final angular speed = wf…

Q: In the figure, two particles, each with mass m cm and mass M = 1.1 kg. The combination rotates…

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Q: The uniform solid block in the figure has mass 47.6 kg and edge lengths a = 0.782 m, b = 1.61 m, and…

A: By perpendicular axis theorem , moment of inertia of block about an axis perpendicular to plane and…

Q: A uniform solid disk of mass m = 3 kg and radius r= 1 m rotates about a fixed axis perpendicular to…

A: Given The mass of the disk is m=3 kg. The radius of the disk is r=1 m. The angular frequency is ω=6…

Q: A wheel of radius 0.343 m, which is moving initially at 31.3 m/s, rolls to a stop in 296 m.…

A: (a) Express the relation for the linear acceleration of the wheel. v2=u2+2aSa=v2-u22S Here, u is the…

Q: A solid, horizontal cylinder of mass 13.2 kg and radius 1.00 m rotates with an angular speed of 8.00…

A: mass of Cylinder= 13.2 kg Radius= 1 m angular speed= 8 rad/s   Putty mass= 0.25 Kg

Q: A uniform solid sphere, of radius R = 1.0 m and mass M = 5.0 kg, rotates freely with a constant…

A: Given : Radius →R=1.0 m Mass →M=5.0 kg  Angular speed →ω=2.0 rad/s

Q: A solid, horizontal cylinder of mass 12.4 kg and radius 1.00 m rotates with an angular speed of 6.00…

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Q: A sanding disk with rotational inertia 9.8 x 10-3 kg·m2 is attached to an electric drill whose motor…

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Q: A rigid object is initially at rest and set into rotational motion under a constant angular…

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Q: A uniform solid cylinder of mass M=2 kg and radius R=0.49 m is given an initial angular speed ω=15…

A: Given data The mass of the solid cylinder is M = 2 kg. The radius of the cylinder is R = 0.49 m.…

Q: A hollow spherical shell of radius R that is rotating about an axis through its center has…

A: Expression for kinetic energy -  EK=12Iω2 Where,  I=Moment of inertia of hollow sphericalI=23MR2ω2…

Q: QUESTION 14 For a solid uniform disk of mass M and radius R that is rolling without slipping, which…

A: Option A is the right answer  It's translational kinetic energy is larger