1. Assignments cont’d…
1. Determine 𝐼 𝑧𝑧 , 𝐼 𝑥𝑦 and the centroid of the square plate shown with
three circular holes cut in it.
a= 100 cm
𝑟 1 =10 𝑐𝑚
𝑟 2 =7 𝑐𝑚
𝑟 3 =4 𝑐𝑚
𝑑 1 =25 𝑐𝑚
𝑑 2 =35 𝑐𝑚
𝑑 3 =30 𝑐𝑚

2. Assignments
2. Determine the mass moment of inertia and centroid of the frustum about the x, y and z axis, the mass of body is 20 kg.
𝑟 1 =120 𝑚𝑚
𝑟 2 =200 𝑚𝑚
ℎ=300 𝑚𝑚

3. ASSIGNMENT 3
The turbine rotor of a ship has a mass of 20 t, has a radius of gyration of 0.6 m and rotates at 3600 rpm. The ship is pitching 10° above and 10° below the horizontal, the motion being simple harmonic and having a period of 12s.The rotor turns in a clockwise direction when viewed from aft. Determine (a) maximum angular velocity of ship during pitching (b) the maximum angular acceleration of ship during pitching (c) the maximum value of the gyroscopic couple stating its plane of action (d) the direction of yaw as the bow rises.

4. ASSIGNMENT 4
The following particulars are given for a motor vehicle: total mass, 1.5 t; wheel base, 3.2 m; track width, 1.5 m; centre of gravity 1.8 m behind the front axle and 0.95 m above road level; moment of inertia of two front wheels, 10 kg 𝑚 2 ; moment of inertia of two rear wheels, 15 kg 𝑚 2 ; moment of inertia of parts turning at engine speed, 2 kg 𝑚 2 ; wheel diameter, 0.64 m, gear ratio from engine to road wheels, 10 to 1. The engine turns in a clockwise direction when viewed from the front of the vehicle. The vehicle travels at a constant speed of 80 km/h and enters a right-hand curve of 150 m radius. Determine: (a) the vertical load on each wheel, taking into account (i) gravitational effects ; (ii) centrifugal effects ; (iii) the gyroscopic effect due to the engine rotation; (b) the rolling couple acting on the vehicle due to the gyroscopic effect of the road wheels.

5. ASSIGNMENT 5
The figure below shows the basic construction of a rate of turn indicator for an aircraft. View A is obtained by looking at the instrument from the starboard (right hand) side of the aircraft and view B is that observed by the pilot when looking straight ahead. The main frame E of the instrument is fixed to the aircraft while frame D can rotate relatively to E about axis XX, its angular position being indicated by the pointer P. The position of frame D relative to frame E is controlled by the two equal springs S which are attached to both frames as shown. These springs have sufficient initial stretch to ensure that they remain in tension as frame D tilts, and any slight inclination which they make with the vertical may be ignored. C is a thin rigid disc of uniform thickness having a mass of 0.3, kg and a radius of 40 mm. It rotates at 8000 rpm on a spindle carried in frame D. When the aircraft is in level flight and is altering course steadily at the rate of 90° in 15 s it is desired that the pointer should read 10° in the appropriate sense indicating the direction of turn. Calculate the necessary stiffness of the springs and determine the direction of spin of the disc, as seen in view A. Show the derivation from first principles of any formula used, indicating where any approximations are made, and explaining clearly how the direction of spin is determined.

6. Assignment 6
The"quick-return" mechanism consists of a crank AB, slider block B, and slotted link CD. If the crank has the angular motion shown, determine the angular motion of the slotted link at this instant.

7. ASSIGNMENT 7
r = 2 m and b = 4.5 m

8. ASSIGNMENT 8

9. ASSIGNMENT 9

10. ASSIGNMENT 10

11. Assignments 11
1. The turning moment diagram for a multi cylinder engine has been drawn to a scale of 1 mm = 4500 N -m vertically and 1 mm = horizontally. The intercepted areas between output torque curve and mean resistance line taken in order from one end are 342, 23, 245, 303, 115, 232, 227, 164 𝑚𝑚 2 , when the engine is running at 150 rpm. If the mass of the flywheel is 1000 kg and the total fluctuation of speed does not exceed 3% of the mean speed, find the minimum value of the radius of gyration.

12. Assignment 12
The figure shows the arrangement of a governor. The central sleeve A does not move axially. The sleeve S has a mass of 18 kg and the frictional resistance to its movement may-be taken as 20 N. There are two right-angled bell-crank levers, each having a ball of mass 4 kg attached to its lower end. The masses of the levers themselves and the rollers on their horizontal arms may be neglected but the dead weight of the balls must not be neglected. The spring has a stiffness of 50 kN/m compression. When the sleeve is in its lowest position, the balls rotate in a circle of 100 mm radius, the ball arms are vertical and the spring force is 550 N. Calculate (a) the speed at which the sleeve will begin to rise from its lowest position, and (b) the range within which the speed must lie when the sleeve is 10 mm above its lowest position.

13. ASSIGNMENT 13
Four masses A, B, C and D are attached to a shaft and revolve in the same plane. The masses are 12 kg, 10 kg, 18 kg and 15 kg respectively and their radii of rotations are 40 mm, 50 mm, 60 mm and 30 mm. The angular position of the masses B, C and D are 60°, 135° and 270° from the mass A. Find the magnitude and position of the balancing mass at a radius of 100 mm.

14. ASSIGNMENT 14
The spacing of the four cylinders A, B, C and D of a vertical in-line engine is 650 mm, 500 mm and 650 mm. The reciprocating masses of the inner cylinders B and C arc 50 kg, and their cranks are at 60° to one another; the stroke is 325 nun and the connecting rods are 600 mm long. Find the magnitudes of the reciprocating masses for the outer cylinders A and D and the relative angular positions of all the cranks if all primary forces and couples are to be balanced. What will be the maximum unbalanced secondary force acting on the base when the engine is run at 375 rev/min.

15. THANK YOU