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 V b, L, α and θ.

(Dec. ’07)[Ans. :V bSinαLcosθ

]

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 :V B = 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 ]

Q13. Find the instantaneous angular velocity of bar AB as shown in the figure.

Engineering Mechanics Problem Sheet – 5 Module - 5 Kinematics of Rigid Bodies

[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 BCeach 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 : V B=274.74mm /s ( ), V C=240mm /s ( ), ωAB=0.9745 rad/sec (Anticlockwise), ωBC=1.216 rad/sec (Anticlockwise). ]

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: V C=0.1875m/ s ( ),V B=0.25m /s ( ), ω AC=1.5 rad/sec (Anticlockwise), ωBC=1.25 rad/sec (Clockwise). ]

Q20. Knowing that at the instant shown in fig. The angular velocity of rod BE is 4 rad/sec counter- clockwise, determine (i) the angular velocity of rod AD and (ii) the velocity of collar D.

Engineering Mechanics Problem Sheet – 5 Module - 5 Kinematics of Rigid Bodies

[Ans:ωAD=4.267 rad/sec (Clockwise), V D=1.3867m / 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:V B=1.8m /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:V C=120 cm / sec ( ),

V D=153.67 cm / sec ( )]

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) V D=720mm /s ( ) ]

Engineering Mechanics Problem Sheet – 5 Module - 5 Kinematics of Rigid Bodies

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 is1.2 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), V B=1.073m /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: V A=237.12mm/s ]