== Consider the helical wire x(t) = cos(t), y(t) = sin(t), z=t,0≤t≤2 whose linear density is 6 = x² + y² + z². 8π (a) the mass of the wire = √2 2+ ☑ 3 (b) the center of mass of the wire xcm Απ 8n 2π+ 3 Απ' Yem 3 8π 0 2π + 3 Zem (2x²+4x) (2) 2+ 3 (c) The moment of inertia I₂ = √2 2+ 8π 3 (d) The radius of gyration k, 1

Solve (xex + y) dx − x dy = 0

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1m radius disk is moving on the inclined surface under no slip condition. the center of the disk has 3m/s velocity and according to the figure, bar BC is pinned to the disk at point C and point B always stays on the ground. 1) find angular velocity of BC. 2) find angular acceleration of BC

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To measure the temperature of a ceramic oven at the college of Arts in PTUK a a thermocouple measurement device is used. The thermocouple has a seebeck coefficient of 60uV/C and has an output voltage of 60mV. When the reference point is 21-C the temperature of the measuring junction is Select one a. none b. 979 C c. 929C d.992C e.927 C.

(3) The Elon Company manufactures parts for an aircraft company using three computerized numerical controlled (CNC) turning centers. The company has to decide which machines are capable of producing a specific part with design specifications of 0.0970 inch ± 0.015 inch. The machines have the following parameters: Machine 1 (x= 0.0995, o = 0.004); Machine 2 ( = 0.1002, o = 0.009); Machine 3 (x = 0.095, o = 0.005). Determine which machines (if any) can produce the products within the design specifications. ||

Water entering the curved pipe at A is discharged at D. The pipe is rotating about A at the constant angular velocity omega=7 rad/s, and the water has a constant speed of v=19 m/s relative to the pipe. Now fill in the blanks below with correct numbers. Αγω သ B 0.54 m r = 0.18 m The magnitude of acceleration of the water just before it is discharged at D= m/s^2 0.30 m