MA1001 Dynamics Tutorial 5(1)

Tutorial 5. Planar motion of a rigid body

Section A: Review Read 2.1 - 2.3 , 2.5 (1),(2), and 2.6 (1),(2). Try questions 2.1-2.5, 2.17-2.19.

Section B: Tutorial Problems 1. Collar A moves in a constant velocity of 900 mm/s to the

right. At the instant when θ = 30°, determine (a) the angular velocity of rod AB, (b) the velocity of collar B.

(BJ 15.34 on page 721) Answer: (a) − 3.68 k , (b) 1017∠−70° (mm/s) 2. In the position shown, bar AB has a constant angular velocity

of 3 rad/s counterclockwise. (a) Determine the angular velocity of bars BD and DE. (b) Determine the angular acceleration of bars BD and DE. (BJ 15.51 on page 723)

Answer: (a) ω2 = − 1.5 k (cw) ,

ω3 = 4 k (ccw)

(b) k5.42 =α , k63 −=α

3. Knowing that at the instant shown the velocity of collar D is

120 mm/s to the left, determine (a) the instantaneous center of rotation of rod BE, (b) the angular velocity of a crank AB and rod BE, (c) the velocity of point E. (BJ 15.62 on page 729)

Answer: (b) 2.7 k (ccw) , 1.2 k (ccw) (c) 239.5∠141.2° (mm/s)

D

B 100 mm

100 mm

125 mm 225 mm

A

E

B

D

A

E

200 mm

100 mm

225 mm

75mm

A

B

70° 30°

300 mm

MA1001 Dynamics Tutorial 5(2)

4. The vertical plate ABED is pinned to rod OA at A and supported by a roller at E which slides in a horizontal slot. In the position shown the velocity of E is 0.7 m/s to the right. Determine (a) the angular velocity of the plate, and (b) the velocities of A, B, and D.

Answer: (a) 0.05 (ccw), (b) 0.5∠-53.13o , 0.806∠-29.74o, 0.3∠0o

5. At a given instant, the cable supporting the pipe has the motion shown. Determine the angular

velocity and angular acceleration of the pipe and the velocity and acceleration of point B located on the pipe. (H 16-143)

Answer: ω = −0.25(rad/s) (cw), α = 0.875(rad/s2) (ccw)

Bv = 1.5∠−90° (m/s), Ba = 0.452∠-85.2 (m/s2)

Additional problems: 2.7, 2.9, 2.11, 2.13, 2.14, 2.23, 2.24

D

B

4 m 8 m

5 m

3 m

A

O

E

B

C D

vC=1.5 m/s

aC = 0.45 m/s2

vD =1.8 m/s

aD = 0.6 m/s2

0.6 m

i

j