Rotational kinetic energy is yet another mass-dependent engineering quantity. An object having a mass moment of inertia I and rotating with angular speed of ? (rad/s) has a rotational kinetic energy, which is equal to 1/2I?2. Consider a cylindrical stainless steel shaft that is 3 ft long and has a diameter of 9 in. What is the volume of the stainless steel shaft (in ft3)? What is the density of stainless steel (in kg/m3)? (See the table below.) Density, Specific Gravity, and Specific Weight of Some Materials (at room temperature or at the specified temperature) Material Density (kg/m3) Specific Gravity Specific Weight (N/m3) Solids Aluminum 2,740 2.74 26,880 Asphalt 2,110 2.11 20,700 Cement 1,920 1.92 18,840 Clay 1,000 1.00 9,810 Fireclay Brick 1,790 @ 100°C 1.79 17,560 Glass (soda lime) 2,470 2.47 24,230 Glass (Lead) 4,280 4.28 41,990 Glass (Pyrex) 2,230 2.23 21,880 Iron (Cast) 7,210 7.21 70,730 Iron (Wrought) 7,700 @ 100°C 7.70 75,540 Paper 930 0.93 9,120 Steel (Mild) 7,830 7.83 76,810 Steel (Stainless 304) 7,860 7.86 77,110 Wood (Ash) 690 0.69 6,770 Wood (Mahogany) 550 0.55 5,400 Wood (Oak) 750 0.75 7,360 Wood (Pine) 430 0.43 4,220 Fluids Standard Air 1.225 0.0012 12 Gasoline 720 0.72 7,060 Glycerin 1,260 1.26 12,360 Mercury 13,550 13.55 132,930 SAE 10W Oil 920 0.92 9,030 Water 1,000 @ 4°C 1.0 9,810 Express the density value in slugs/ft3. What is the mass of the shaft (in slugs)? Determine the mass moment of inertia of the shaft about its longitudinal axis (in slugs · ft2). Iz − z = slugs · ft2 Express the Iz − z value in U.S Customary units of lbm · ft2 and lbm · in2. Express the Iz − z value in SI units of kg · m2. What is the angular speed of 170 rpm in rad/s? Determine the rotational kinetic energy in ft · lbf. Express the rotational kinetic energy in J.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

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Rotational kinetic energy is yet another mass-dependent engineering quantity. An object having a mass moment of inertia I and rotating with angular speed of ? (rad/s) has a rotational kinetic energy, which is equal to

1/2I?².

Consider a cylindrical stainless steel shaft that is 3 ft long and has a diameter of 9 in.

What is the volume of the stainless steel shaft (in ft³)?

What is the density of stainless steel (in kg/m³)? (See the table below.)

Density, Specific Gravity, and Specific Weight of Some Materials (at room temperature or at the specified temperature)

	Material	Density (kg/m³)	Specific Gravity	Specific Weight (N/m³)
Solids	Aluminum	2,740	2.74	26,880
Asphalt	2,110	2.11	20,700
Cement	1,920	1.92	18,840
Clay	1,000	1.00	9,810
Fireclay Brick	1,790 @ 100°C	1.79	17,560
Glass (soda lime)	2,470	2.47	24,230
Glass (Lead)	4,280	4.28	41,990
Glass (Pyrex)	2,230	2.23	21,880
Iron (Cast)	7,210	7.21	70,730
Iron (Wrought)	7,700 @ 100°C	7.70	75,540
Paper	930	0.93	9,120
Steel (Mild)	7,830	7.83	76,810
Steel (Stainless 304)	7,860	7.86	77,110
Wood (Ash)	690	0.69	6,770
Wood (Mahogany)	550	0.55	5,400
Wood (Oak)	750	0.75	7,360
Wood (Pine)	430	0.43	4,220
Fluids	Standard Air	1.225	0.0012	12
Gasoline	720	0.72	7,060
Glycerin	1,260	1.26	12,360
Mercury	13,550	13.55	132,930
SAE 10W Oil	920	0.92	9,030
Water	1,000 @ 4°C	1.0	9,810

Express the density value in slugs/ft³.

What is the mass of the shaft (in slugs)?

Determine the mass moment of inertia of the shaft about its longitudinal axis (in slugs · ft²).

I_z − z = slugs · ft²

Express the I_{z − z}value in U.S Customary units of lbm · ft² and lbm · in².

Express the I_{z − z}value in SI units of kg · m².

What is the angular speed of 170 rpm in rad/s?

Determine the rotational kinetic energy in ft · lbf.

Express the rotational kinetic energy in J.

Expert Solution

Step 1

Note: As per guideline only the first 3 question in a subpart question will be solved for the remaining parts submit the question again and ask for remaining part only

Given data:

cylindrical steel shaft length L = 3 ft = 36 in = 0.9144 m

cylindrical steel shaft diameter D = 9 in = 0.75 ft = 0.2286 m

Find:

(a) Volume of the stainless steel shaft

(b) density of stainless steel

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Follow-up Question

Determine the mass moment of inertia of the shaft about its longitudinal axis (in slugs · ft²).

I_z − z =

Express the I_{z − z}value in U.S Customary units of lbm · ft² and lbm · in².

Express the I_{z − z}value in SI units of kg · m².

What is the angular speed of 170 rpm in rad/s?

Determine the rotational kinetic energy in ft · lbf.

Express the rotational kinetic energy in J.

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