### Explanation of Rigid Assembly Angular Speed#### Problem StatementThe image depicts a rigid assembly consisting of a thin hoop and a thin radial rod. Here are the details of the assembly:- **Hoop:** - Mass \( m = 0.30 \, \text{kg} \) - Radius \( R = 0.17 \, \text{m} \)- **Rod:** - Length \( L = 2R \) - Mass \( m = 0.30 \, \text{kg} \)The assembly is initially upright. A slight nudge causes it to rotate around a horizontal axis, intersecting the plane of the rod and hoop through the lower end of the rod. The energy imparted to the system by this nudge is assumed to be negligible.#### ObjectiveDetermine the assembly's angular speed about the rotation axis as it transitions through the upside-down (inverted) position.#### Diagram Explanation- The diagram illustrates the assembly with the hoop on top of the rod.- The **rotation axis** is indicated at the lower end of the rod. #### SolutionA numerical field with the solution is present:- **Number:** 9.23- **Units:** rad/s (radians per second)This value represents the calculated angular speed of the assembly when inverted.This problem involves concepts of rotational dynamics, particularly the conservation of energy in a rotating system.

Given :Mass of hoop, mh=0.30 kgRadius of hoop, R=0.17 mMass of rod, mr=0.30 kgLength of the rod, L=2R L=2 x 0.17=0.34 mMoment of inertia of hoop about axis,IH=Moment of inertial about diameter +ma2 (Using parallel axis theorem)a=R+L =3R = 3 x 0.17=0.51 mId=MR22IH=0.30 x 0.1722+0.30 x 0.512 =0.00433 + 0.078 = 0.08236 kgm2Moment of inertia of rod about axis=MI of rod about end.Ir=mrL23=0.30 x 0.3423=0.01156=11.56 x 10-3 kgm2Net moment of inertia of the system,I=Ir+IHI=11.56 x 10-3 kgm2+0.08236 kgm2I=0.093 kgm2According to conservation of energy,Lose in PE=Gain in KEmhgHh+mrgHr=I2ω2Hh=2 L + 2 R=2 x 0.34 + 2 x 0.17 =0.68+0.34=1.02Hr=2 x L2+R= 2 x 0.342+0.17=0.51m⇒ω=2 x (0.30 x 9.8 x 1.02 + 0.30x9.8 x 0.51)0.093ω=2(2.99+1.49)0.093ω=2 x 4.480.093ω=96.344ω=9.81 rad/s

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Physics

The figure shows a rigid assembly of a thin hoop (of mass m = 0.30 kg and radius R = 0.17 m) and a thin radial rod (of length L = 2R and also of mass m = 0.30 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? Hoop Rod Rotation аxis Number 9.23 Units rad/s

The figure shows a rigid assembly of a thin hoop (of mass m = 0.30 kg and radius R = 0.17 m) and a thin radial rod (of length L = 2R and also of mass m = 0.30 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? Hoop Rod Rotation аxis Number 9.23 Units rad/s

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)...

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