1. Problem 12.128 Pin B weighs 4 oz and is free to slide
in a horizontal plane along the rotating
arm OC and along the circular slot DE
of radius b = 20 in. Neglecting friction
and assuming that q = 15 rad/s and
q = 250 rad/s2 for the position q = 20o,
determine for that position (a) the
radial and transverse components of
the resultant force exerted on pin B,
(b) the forces P and Q exerted on pin
B, respectively, by rod OC and the wall
of slot DE. . q b r O A B C D E

2. . eq v = r er + r q eq er a = (r - r q 2 ) er + (r q + 2 r q ) eqb r O A B C D E
Problem
Solving Problems on Your Own
Pin B weighs 4 oz and is free to slide
in a horizontal plane along the rotating
arm OC and along the circular slot DE
of radius b = 20 in. Neglecting friction
and assuming that q = 15 rad/s and .
q = 250 rad/s2 for the position q = 20o, determine for that position
(a) the radial and transverse components of the resultant force
exerted on pin B, (b) the forces P and Q exerted on pin B,
respectively, by rod OC and the wall of slot DE.
1. Kinematics: Examine the velocity and acceleration of the
particle. In polar coordinates:
v = r er + r q eq
a = (r - r q 2 ) er + (r q + 2 r q ) eq .
r = r er eq er q

3. q b r O A B C D E
Problem
Solving Problems on Your Own
Pin B weighs 4 oz and is free to slide
in a horizontal plane along the rotating
arm OC and along the circular slot DE
of radius b = 20 in. Neglecting friction
and assuming that q = 15 rad/s and .
q = 250 rad/s2 for the position q = 20o, determine for that position
(a) the radial and transverse components of the resultant force
exerted on pin B, (b) the forces P and Q exerted on pin B,
respectively, by rod OC and the wall of slot DE.
2. Kinetics: Draw a free body diagram showing the applied
forces and an equivalent force diagram showing the vector
ma or its components.

4. q b r O A B C D E
Problem
Solving Problems on Your Own
Pin B weighs 4 oz and is free to slide
in a horizontal plane along the rotating
arm OC and along the circular slot DE
of radius b = 20 in. Neglecting friction
and assuming that q = 15 rad/s and .
q = 250 rad/s2 for the position q = 20o, determine for that position
(a) the radial and transverse components of the resultant force
exerted on pin B, (b) the forces P and Q exerted on pin B,
respectively, by rod OC and the wall of slot DE.
3. Apply Newton’s second law: The relationship between the
forces acting on the particle, its mass and acceleration is given
by S F = m a . The vectors F and a can be expressed in terms of
either their rectangular components or their radial and transverse
components. With radial and transverse components:
S Fr = m ar = m ( r - r q 2 ) and S Fq = m aq = m ( r q + 2 r q ) . .

5. r = 2 b cos q q = 20o r = - 2 b sin q q q = 15 rad/sE
Problem Solution
Kinematics. 2q b r O A B q
r = 2 b cos q
r = - 2 b sin q q
r = - 2 b sin q q - 2 b cos q q 2
q = 20o
q = 15 rad/s
q = 250 rad/s2 . . . . . .

6. r = 2 b cos q, r = - 2 b sinq q, r = - 2 b sinq q - 2 b cosq q 2A B q
Problem Solution . . .
r = 2 b cos q, r = - 2 b sinq q, r = - 2 b sinq q - 2 b cosq q 2 . .
For: b = 20/12 ft, q = 20o,
q = 15 rad/s q = 250 rad/s2
r = 2 (20/12 ft) cos 20o = ft
r = - 2 (20/12 ft) sin 20o (15 rad/s) = ft/s
r = -2(20/12 ft) sin 20o (250 rad/s2 ) - 2(20/12 ft) cos 20o (15 rad/s)2
r = ft/s2 . . . . . .

7. = Problem 12.128 Solution r C (a) Radial and transverse B Dq b r O A B C D E
(a) Radial and transverse
components of the resultant force
exerted on pin B.
Kinetics; draw a free body diagram. r O A B q Fr Fq
mar
maq =

8. = + SFr = mar: Fr = m ( r - r q2 )
Apply Newton’s second law.
Problem Solution r O A B q Fr Fq
mar
maq =
SFr = mar: Fr = m ( r - r q2 )
Fr = [ ( 3.13 )(152 )] = lb Fr = lb
+ SFq = maq: Fq = m ( r q + 2 r q )
Fq = [(3.13)(250) + 2 (-17.1)(15)] = 2.1 lb . .
(4/16)
32.2 . . .
(4/16)
32.2
Fq = 2.10 lb

9. = Fr = - Q cos q Fq = - Q sin q + P -13.16 = - Q cos 20ob r O A B C D E
Problem Solution Fq Fr Q q = r B r q B q q q P A O A O
Fr = - Q cos q
= - Q cos 20o
Q = lb
Fq = - Q sin q + P
2.10 = sin 20o + P
P = 6.89 lb
20o
40o