Engineering Mechanics
Problem Sheet – 5
Module - 5
Kinematics of Rigid Bodies
Q1. Two wheels are attached to the end of rod ‘AB’
as shown in figure. Find the angular velocity of the
rod in terms of 𝑉𝑏 , L, α and θ.
𝑽 𝐒𝐢𝐧𝛂
(Dec. ’07)[Ans. : 𝑳𝒃𝑪𝒐𝒔 𝜽 ]
Q2. A rod AB 26 m long leans against a vertical wall. The end ‘A’ on the floor is drawn away
from the wall at a rate of 24 m/s. When the end ‘A’ of the rod is 10 m from the wall,
determine the velocity of the end ‘B’ sliding down vertically and the angular velocity of rod
AB.
(May ’09)[Ans.: VB = 10 m/s, ωAB= 1 r/s]
Q3. Block ‘D’ shown in figure moves with a
speed of 3m/s. Determine the angular
velocities of link BD and AB and the
velocity of point B at the instant shown. Use
method of instantaneous center of zero
velocity.[Ans.:ωBD=5.3r/s , VB=2.12 m/s,
ωAB=5.3 r/s ]
Q4. A wheel of radius 0.75 m rolls without slipping on a horizontal
surface to the right. Determine the velocities of the points P and Q
shown in figure when the velocity of centre of the wheel is 10 m/s
towards right. (Dec. ’09) [Ans.: VP= 14.14 m/s, VQ= 20 m/s]
Q5. In the mechanism shown, find the velocity of point C
and angular velocity of link BC if the angular velocity
of link AB is 4 rad/sec. Solve the problem when link
AB and link BC make an angle of 45° with the
horizontal as shown in figure.
(May ’10) [Ans.: ωBC=5 rad/s
, VC=7.07 m/s (→)]
Engineering Mechanics
Problem Sheet – 5
Module - 5
Kinematics of Rigid Bodies
Q6. Locate the instantaneous centre of rotation for the link ABC
and determine velocity of point B and C. Angular velocity
of rod OA is 15 rad/sec counter clockwise. Length of OA is
200 mm, AB is 400 mm and BC is 150 mm.
(Dec. ’10)[Ans.: VB = 16234 mm/s, VC =21770 mm/s]
Q7. Rod AB of length 3m is kept on
smooth planes as shown in the figure.
The velocity of the end A is 5 m/sec.
along the inclined plane. Locate the
ICR and find the velocity of the end B.
[Ans.: VB = 5.24 m/s (→)]
Q8. In a crank and connecting rod mechanism, the
length of crank and the connecting rod are
300 mm and 1200 mm respectively. The
crank is rotating at 180 rpm. Find the velocity
of piston, when the crank is at an angle of 45°
with the horizontal. [Ans.: VA = 4.71 m/s (→)]
Q9. At the position shown in figure the crank AB has angular
velocity of 3rad/sec clockwise. Find the velocity of
slider C and the point D at the instant shown.
AB = 100 mm
[Ans.: VC =400mm/s (→), VD = 721.12 mm/s ( )]
Engineering Mechanics
Problem Sheet – 5
Module - 5
Kinematics of Rigid Bodies
Q10. Collar B moves up with a constant velocity VB = 2 m/s.
Rod AB is pinned at B. Find out angular velocity of AB and
velocity of A.
[Ans.: ω1=1.229 rad/s
, VA=1.63 m/s (
)]
Q11. A rod AB 25 m long is placed in a
parabolic drum as shown in the figure. End A
of the rod slides rightwards with 41 m/sec.
Find the velocity of end B and angular velocity
of the rod at the given instant.
[Ans :𝑽𝑩 = 25.63 m/s
𝝎𝑨𝑩 = 1.6 r/s ]
Q12. A roller of radius 8 cm rides between two
horizontal bars moving in the opposite
direction as shown in the figure. Locate the
instantaneous centre of velocity and give its
distance from B. Assume no slip conditions at
the points A and B. Locate the position of the
instantaneous center where both the bars are
moving in the same direction.
[Ans : Case 1 : IB = 0.6 m, Case 2 : IB = 0.24 m ]
Engineering Mechanics
Problem Sheet – 5
Module - 5
Kinematics of Rigid Bodies
Q13. Find the instantaneous angular velocity
of bar AB as shown in the figure.
[Ans: 𝝎𝑩𝑪 = 𝟐 𝒓𝒂𝒅/ sec]
Q14. If rod AB is rotating with the angular
velocity 𝜔𝐴𝐵 = 12 r/s determine the angular
velocity of rods BC and CD at the instant
shown in figure.
[Ans: 𝝎𝑩𝑪 = 𝟏. 𝟑𝟑 𝒓/s Clockwise, 𝝎𝑪𝑫 = 𝟗. 𝟗𝟕𝟐 𝒓𝒂𝒅/sec Anticlockwise]
Q15. In the mechanism shown in fig. angular velocity
of rod DC is 30Oper second. Determine angular velocity
of CB and AB.
[Ans : 𝝎𝑩𝑪 = 𝟎. 𝟏𝟗𝟒 𝒓𝒂𝒅/sec (Anticlockwise), 𝝎𝑨𝑩 =
𝟎. 𝟓𝟖𝟐 𝒓𝒂𝒅/sec (Anticlockwise). ]
Q16. In the position shown in Fig. rod AB is
horizontal and has angular velocity 1.8 rad/sec in
clockwise sense. Determine angular velocities of
BC and DC.
[Ans : 𝝎𝑩𝑪 = 𝟎. 𝟕𝟐 𝒓𝒂𝒅/sec (Anticlockwise),
𝝎𝑪𝑫 = 𝟏. 𝟖 𝒓𝒂𝒅/sec (Anticlockwise). ]
Engineering Mechanics
Problem Sheet – 5
Module - 5
Kinematics of Rigid Bodies
Q17. A bar BC slides at C in a collar by 4 m/sec
velocity as shown in fig. The other end B is
pinned on a roller. Find angular velocity of bar
BC and the roller.
[Ans : 𝝎𝑩𝑪 = 𝟎. 𝟑𝟖𝟔 𝒓𝒂𝒅/sec (Clockwise),
𝝎𝑹𝒐𝒍𝒍𝒆𝒓 = 𝟏. 𝟖𝟗𝟏 𝒓𝒂𝒅/sec (Clockwise). ]
Q18. In the mechanism shown in the fig.
Collars A and C slide on horizontal rods.
While B on a velocity rod. Link AB and BC
each 300 mm long, are hinged to the
collars. At the instant shown VA = 100
mm/sec to the left and Ɵ = 70o. Find (i) the
velocity of collar B and C and (ii) the
angular velocity of AB and BC.
[Ans : 𝑽𝑩 = 𝟐𝟕𝟒. 𝟕𝟒 𝒎𝒎/𝒔 ( ), 𝑽𝑪 =
𝟐𝟒𝟎 𝒎𝒎/𝒔 ( ), 𝝎𝑨𝑩 = 𝟎. 𝟗𝟕𝟒𝟓 𝒓𝒂𝒅/sec (Anticlockwise),
𝟏. 𝟐𝟏𝟔 𝒓𝒂𝒅/sec (Anticlockwise). ]
𝝎𝑩𝑪 =
Q19. In the given figure, C is constrained to move
in the vertical slot. A and B move on horizontal
floor. Rod CA and CB are connected with smooth
hinges. If VA = 0.45m/sec to the right. Find velocity
of C and B. Also find the angular velocity of the two
rods.
[Ans: 𝑽𝑪 = 𝟎. 𝟏𝟖𝟕𝟓 𝒎/𝒔 ( ), 𝑽𝑩 = 𝟎. 𝟐𝟓𝒎/𝒔 ( ),
𝝎𝑨𝑪 = 𝟏. 𝟓 𝒓𝒂𝒅/sec (Anticlockwise), 𝝎𝑩𝑪 = 𝟏. 𝟐𝟓 𝒓𝒂𝒅/sec (Clockwise). ]
Engineering Mechanics
Problem Sheet – 5
Module - 5
Kinematics of Rigid Bodies
Q20. Knowing that at the instant shown in fig. The
angular velocity of rod BE is 4 rad/sec counterclockwise, determine (i) the angular velocity of
rod AD and (ii) the velocity of collar D.
[Ans: 𝝎𝑨𝑫 = 𝟒. 𝟐𝟔𝟕 𝒓𝒂𝒅/sec (Clockwise), 𝑽𝑫 =
𝟏. 𝟑𝟖𝟔𝟕 𝒎/𝒔 ( )]
Q21. In the device shown in fig. Find
the velocity of point B and angular
velocity of both the rods. The wheel is
rotating at 2 rad/sec Anticlockwise.
[Ans:𝑽𝑩 = 𝟏. 𝟖 𝒎/𝒔 ( ),
𝝎𝑨𝑩 = 𝟐 𝒓𝒂𝒅/sec (Antilockwise),
𝝎𝑩𝑪 = 𝟔 𝒓𝒂𝒅/sec (Antilockwise) ]
Q22. A bar AB, 24 cm long, is hinged to a
wall at A as shown in fig. Another bar CD 32
cm long is connected to it by a pin at B such
that CB =12cm and BD = 20 cm. At the instant
shown, (AB is perpendicular to CD) the
angular velocities of the bars are 𝜔𝐴𝐵 =
4 𝑟𝑎𝑑/sec. and 𝜔𝐶𝐷 = 6 𝑟𝑎𝑑/sec. Determine
the liner velocity of C and D. (Hint Bar CD is in
plane motion).
[Ans:𝑽𝑪 = 𝟏𝟐𝟎 𝒄𝒎/𝒔𝒆𝒄 ( ),
𝑽𝑫 = 𝟏𝟓𝟑. 𝟔𝟕 𝒄𝒎/𝒔𝒆𝒄 (
)]
Engineering Mechanics
Problem Sheet – 5
Module - 5
Kinematics of Rigid Bodies
Q23. At the position shown in fig. the crank
AB has angular velocity of 3 rad/sec
clockwise. Find the angular velocity of CD
and the velocity of point D at the instant
shown.
[Ans:𝝎𝑪𝑫 = 𝟒 𝒓𝒂𝒅/sec (Antilockwise)
𝑽𝑫 = 𝟕𝟐𝟎 𝒎𝒎/𝒔 (
)]
Q24. In the mechanism shown in Fig.
rod AB is horizontal, CD is vertical.
End A is guided in an inclined slot
having slope 3 in 4. If velocity of A is
1.2 m/sec up the slot. Determine (i)
angular velocity of AB & CD and (ii)
liner velocity of B.
Given AD =450mm, BD=300mm, CD=
360mm, VA= 1.2 m/sec.
[Ans: 𝝎𝑨𝑩 = 𝟏. 𝟔 𝒓𝒂𝒅/sec (Clockwise), 𝝎𝑪𝑫 = 𝟐. 𝟔𝟕 𝒓𝒂𝒅/sec (Clockwise),
𝑽𝑩 = 𝟏. 𝟎𝟕𝟑 𝒎/𝒔 ]
Q25. The crank BC of a slider crank
mechanism is rotating at a
constant speed of 30 rpm
clockwise as shown in the figure.
Determine the velocity of the cross
head A at the given instant.
[Ans: 𝑽𝑨 = 𝟐𝟑𝟕. 𝟏𝟐 𝒎𝒎/𝒔 ]