eˆt
Sol. 1 V A  (OA) eˆt
𝑒𝑛
0.8  0.1
  8rads 1

 
a B  a O  a rel    OB      OB  2   V rel
a B  a n e n  at e t
an e n  at et   2OB  e n   OB  e t
tan  
at

 2  0.6
an 
  38.4 rads 2

Sol. 2
vB  vO  vrel  OB  OB
vB  0
v A  vB  vrel  BA  BA
v A  BAkˆ  BA(  cos iˆ  sin  ˆj )
v Aiˆ  0  BABA (  cos iˆ  sin  ˆj )
v A  0, and BA  0
aB  aO  arel  OB  OB  OB  OB  OB  2OB  vrel
aB  3kˆ  0.4iˆ
aB  1.2 ˆj
a A  aB  arel  BA  BA  BA   BA  BA  2BA  vrel
a Aiˆ  1.2 ˆj   BAkˆ  0.5(  cos iˆ  sin  ˆj )
a A  1.6iˆ m / s 2
  4kˆ rad / s 2
BA
𝑦
𝑥
𝜑
Sol.3
v A  v A cos(30)eˆn  v A sin(30)eˆt
vB  vB eˆt
eˆn
AB   AB(cos(42.044)eˆn  sin(42.044)eˆt )
vB  v A  vrel    AB
Comparing coefficients of 𝑒𝑛
v A cos(30)

AB sin(42.024)
 3.2341rad / s
aB  aBn eˆn  aBt eˆt
eˆt
12.0240
vB2
a 
 38.407 m / s 2
r
aB  a A  arel      AB  2  vrel    AB
n
B
aBn eˆn  aBt eˆt   2 ( AB cos(42.024)eˆn  AB sin(42.024)eˆt )   ( AB cos(42.024)eˆt  AB sin(42.024)eˆn )
Comparing coefficient of 𝑒𝑛 and 𝑒𝑡
38.407   2 AB cos(42.024)   AB sin(42.024)
ˆ
  36.211krad
/ s2
aBt   2 AB sin(42.024)   AB cos(42.024)
aBt  23.88m / s 2
Sol.4
V A  V B  V rel    BA
0.8i  -0.6i -  k  0.26 j;   5.4 rads -1
a A  a B    BA      BA
( a A - a B  0.26 i - 0.26 2 j ) iˆ
( a A - a B )t  0.26 i
  7.69 rad / s 2
( a A  a O    OA      OA) iˆ
( a A )t  aO i  0.1 i
( aO  0.1 )  2; aO  1.23ms -2
a P  a O    OP      OP
 1.23i - 4.7i -1.23 j
a P  3.62m / s 2
Sol.5
v A  vo  vrel    OA
v A  100iˆ  5kˆ  (36iˆ  25 ˆj )
v A  225iˆ  180 ˆj mm / s
a A  ao  arel    OA      OA  2  vrel
a A  150iˆ  3kˆ  (36iˆ  25 ˆj )  5kˆ  5kˆ  (36iˆ  25 ˆj )  2  5k  (100i )
a A  675iˆ  1733 ˆj mm / s 2
Sol.5 V C   r
6.94iˆ  k  60 j
6.94
 0.115rads 1
60
(V P ) A  V C  V rel   CA

 6.94i  1.5i  1.15 j  1.5i  5.44i  1.15 j m / s
(V P )C  V C  V rel  5.44i m / s
(V P ) B  V C  V rel   CB  5.44i  1.15 j m / s
Sol.7
v A  vC  vrel  CB  rCA
v A  0  0  4kˆ  ( 0.12) ˆj  0.48iˆ
y
v A '  vO  vrel  OB  rOA
v A '  0  OAkˆ  0.12iˆ  0.12OA ˆj
v A  v A '  vrel
0.48iˆ  0.12OA ˆj  vrel (cos 45iˆ  sin 45 ˆj )
vrel  0.6788 m / s
OA  4 rad / s
x
a A  aC  arel   riˆ   2 rjˆ
a A  1.92 ˆj m / s 2
a A  aO  arel  ODE  CA  ODE  ODE  CA  2  ODE  vrel
arel  arel (cos(45)iˆ  sin(45) ˆj )
a A  arel (cos(45)iˆ  sin(45) ˆj )  ODE kˆ  0.12iˆ  ( 4kˆ)  ( 4kˆ)  (0.12iˆ)  2  ( 4kˆ)  (0.48 2(cos(45)iˆ  sin(45) ˆj )
1.92 ˆj  arel (cos(45)iˆ  sin(45) ˆj )  0.12 ˆj  1.92iˆ  3.84( iˆ  ˆj )
Comparing the coefficients of 𝑖 and 𝑗
i:
0
arel
 1.92  3.84
arel
2
 2.715m / s 2
j:
1.92 
  64rad / s 2
2.715
 0.12  3.84
2