Answered: A stationary horizontal plate is…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

A stationary horizontal plate is attached to the ceiling by means of
a fixed vertical tube. A wheel of radius aa and mass mm is mounted on a light axle ACAC that is attached by means of a clevis at AA to a rod ABAB fitted inside the vertical tube. The rod ABAB is made to rotate with a constant angular velocity ΩΩ causing the wheel to roll on the lower face of the stationary plate. Determine the minimum angular velocity ΩΩ for which contact is maintained between the wheel and the plate. Consider the particular cases ( aa ) when the mass of the wheel is concentrated in the rim, (b) when the wheel is equivalent to a thin disk of radius aa

also extend the problem using Kinematic and Kinetic analysis

В
Rotating -
rod
Ω
Fixed -
tube
D
Stationary plate
a
A
-R-

18.97 A stationary horizontal plate is attached to the ceiling by means of
a fixed vertical tube. A wheel of radius a and mass m is mounted
1210 Kinetics of Rigid Bodies in Three Dimensions
B
a rod ÅB fitted inside the vertical tube. The rod AB is made to
rotate with a constant angular velocity N causing the wheel to roll
on the lower face of the stationary plate. Determine the minimum
angular velocity n for which contact is maintained between the
wheel and the plate. Consider the particular cases (a) when the
mass of the wheel is concentrated in the rim, (b) when the wheel
is equivalent to a thin disk of radius a.
Rotating.
rod
Fixed
tube
Stationary plate
18.98 Assuming that the wheel of Prob. 18.97 weighs 8 lb, has a radius
a = 4 in., and a radius of gyration of 3 in., and that R = 20 in.,
determine the force exerted by the plate on the wheel when 2
25 rad/s.
18.99 A thin disk of mass m = 4 kg rotates with an angular velocity
V; with respect to arm ABC, which itself rotates with an angular
velocity V, about the y axis. Knowing that Vị = 5 rad/s and Va =
15 rad/s and that both are constant, determine the force-couple
system representing the dynamic reaction at the support at A.
Fig. P18.97
450 mm
18.100 An experimental Fresnel-lens solar-energy concentrator can rotate
about the horizontal axis AB which passes through its mass center G.
It is supported at A and B by a steel framework which can rotate
about the vertical y axis. The concentrator has a mass of 30 Mg, a
radius of gyration of 12 m about its axis of symmetry CD, and a radius
of gyration of 10 m about any transverse axis through G. Knowing
that the angular velocities V, ánd V, have constant magnitudes equal
to 0.20 rad/s and 0.25 rad/s, respectively, determine for the position
u = 60° (a) the forces exerted on the concentrator at A'and B,
(b) the couple Mak applied to the concentrator at that instant.
150 mm
205 mm
Fig. P18.99
16 m
16 m
Fig. P18.100

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