978-0073398242 Chapter 18 Solution Manual Part 16

PROBLEM 18.95

Two disks, each of mass 5 kg and radius 300 mm, spin as shown at

the rate 11200 rpm



 about a rod AB of negligible mass which

rotates about the horizontal z axis at the rate 260 rpm.





(a) Determine the dynamic reactions at points C and D. (b) Solve part

a assuming that the direction of spin of disk A is reversed.

PROBLEM 18.95 (Continued)

2

(b) For disk A: 12 1 2

,

AAyz

II





   

j

kH

j

k

1, 0



PROBLEM 18.96

Two disks, each of mass 5 kg and radius 300 mm, spin as shown at

the rate 11200 rpm



 about a rod AB of negligible mass which

rotates about the horizontal z axis at the rate 2.



Determine the

maximum allowable value of 2



if the magnitudes of the dynamic

reactions at points C and D are not to exceed 350 N each.



PROBLEM 18.96 (Continued)

2

PROBLEM 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 on a light

axle AC which is attached by means of a clevis at A to a rod AB fitted

inside the vertical tube. The rod AB is made to rotate with a constant

angular velocity  causing the wheel to roll on the lower face of the

stationary plate. Determine the minimum angular velocity  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.

PROBLEM 18.97 (Continued)

Equating moments about A:

()G

RW

R

 

ijH



PROBLEM 18.98

Assuming that the wheel of Problem 18.97 weights 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   25 rad/s.

PROBLEM 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 on a light axle AC which is attached by means of a clevis at A to

a rod AB fitted inside the vertical tube. The rod AB is made to rotate with

a constant angular velocity  causing the wheel to roll on the lower face

of the stationary plate. Determine the minimum angular velocity  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.

PROBLEM 18.98 (Continued)

Taking moments about A:

()

G

RDW

  

ijjH



PROBLEM 18.99

A thin disk of mass 4 kgm



rotates with an angular velocity 2



with respect to arm ABC, which itself rotates with an angular

velocity 1



about the y axis. Knowing that



5 rad/s



and

215 rad/s



 and that both are constant, determine the force-couple

system representing the dynamic reaction at the support at A.

22





4

1(4)(0.150 m) 0.0225 kg m

xy

PROBLEM 18.99 (Continued)

(4)( 11.25 ) (45 N)

C

m aii

Free body and kinetic diagrams