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Moment Project
1.
1 m y
2.
2
3.
3
4.
4 (Rigid body)
(translation) (Rotation)
5.
5 (Linear Momentum ; p
) vmp r v p (Circular Momentum) siniii iii prL prL
6.
6 ( v r iiii vrmrpL
sin s =r dt dr dt d r dt rd dt ds v )( =0 rv dt d
7.
7 ( 2 iii rmL n i iirmL 1 2
8.
8 “0” 2 2 1 iik vmE v =
r 2 )( 2 1 iik rmE n i iik rmE 1 2 2 1 o mi vi m1 m2 m3 m4 mi r1 r2 r3 r4 ri
9.
9 (Moment of inertial;
I) n i iirmK 1 2 2 1 n i iirm 1 2 n i iirmL 1 2 (Moment of inertial; I) n i iirmI 1 2 kg m2
10.
10 (Torque) ( ) ” Torque” F Fr F r sinrF F
11.
11 TiT amF Fri 2 )()( iiiiTii
rmmrramrrF F mi o mi F ri t s sinFri F r s = r v = rd /dt = r aT= r I
12.
12 2 mrI I1 I2 I4 I3 I5 I6 321 IIIIsys n i iisys
rmI 1 2
13.
13 (Homogenous) dm r dm dmrI 2 V dm
= dV
14.
14 rd m R ddrrTdV R 0 2 0 dm = dV =
Tdr2=2 Trdr r dr R rdrTdV 2 dv r 1 22 0 32 )( 2 1 2 RTRdrTrdmrI R 2 2 1 mRI R2T = V =m
15.
15 ( dm dr rddz R1 R2 2 1 2 2 2 0 0 2 1 RRZdzdrdrm dzdrrddVdm R R Z rdmI dzrdrdrdVrI
22 2 1 2 2 2 1 2 2 4 1 4 2 4 3 2 0 3 2 0 0 3 224 2 2 2 1 2 1 2 1 2 1 RRRR Z RR Z r Z drrZdrdrZdzdrdrI R R R R R R R R Z )( 22 22 RRzm )( 2 1 2 1 2 2 RRmI
16.
16 2 2 t y a r a )( agmT rT I
17.
17
18.
18
19.
19 y m t m y
20.
20 m=5g m = 5 y
= 80.00 m y 3 start 3 start 7.7 s
21.
21 m=10g m =10 y =
80.00 m y 3 start 3 start 5.5 s
22.
22 m=15g m = 15 y
= 80.00 m y 3 start 3 start 4.6s
23.
23 m=20g m = 20 y
= 80.00 m y 3 start 3 start 3.9 s
24.
24 m=25g m = 25 y
= 80.00 m y 3 start 3 start 3.5s
25.
25
26.
26 y m t m y
27.
27 m=5g m = 5 y
= 80.00 m y 3 start 3 start 6.3 s
28.
28 m=10g m =10 y =
80.00 m y 3 start 3 start 4.45 s
29.
29 m=15g m = 15 y
= 80.00 m y 3 start 3 start 3.65 s
30.
30 m=20g m = 20 y
= 80.00 m y 3 start 3 start m 3.15 s
31.
31 m=25g m = 25 y
= 80.00 m y 3 start 3 start 2.8 s
32.
32 2 22 m/s022.0 00.6 8000.022 t y a 2 /419.0 0525.0 022.0 srad r a N108.97 )022.08.9(1010)( 3 3 agmT N.m1013.5 108.971025.5 3 32 rT 23 3 mkg102.12 419.0 1013.5 I
33.
33 รัศมีแกนหมุนr 0.0525เมตร พิมพ์ข้อมูลช่องสีชมพู ระยะการเคลื่อนที่y
0.8000เมตร มวล(g) มวล(kg) เวลา(เฉลี่ย) ความเร่งa ความเร่งเชิงมุม แรงตึงT ทอร์ก โมเมนต์ฯI 5.5 0.0055 7.70 0.027 0.514 5.38E-02 2.82E-03 5.49E-03 10.5 0.0105 5.50 0.053 1.007 1.02E-01 5.37E-03 5.33E-03 15 0.015 4.60 0.076 1.440 1.46E-01 7.66E-03 5.32E-03 20 0.02 3.90 0.105 2.004 1.94E-01 1.02E-02 5.08E-03 25 0.025 3.50 0.131 2.488 2.42E-01 1.27E-02 5.10E-03 เสร็จแล้วปิดโปรแกรม excelเพื่อทาตอนต่อไป (m)
34.
34 รัศมีแกนหมุนr 0.0525เมตร พิมพ์ข้อมูลช่องสีชมพู ระยะการเคลื่อนที่y
0.8000เมตร มวล(g) มวล(kg) เวลา(เฉลี่ย) ความเร่งa ความเร่งเชิงมุม แรงตึงT ทอร์ก โมเมนต์ฯI 5 0.005 6.30 0.040 0.768 4.88E-02 2.56E-03 3.34E-03 10 0.01 4.45 0.081 1.539 9.72E-02 5.10E-03 3.32E-03 15 0.015 3.65 0.120 2.288 1.45E-01 7.62E-03 3.33E-03 20 0.02 3.15 0.161 3.071 1.93E-01 1.01E-02 3.30E-03 25 0.025 2.80 0.204 3.887 2.40E-01 1.26E-02 3.24E-03 เสร็จแล้วปิดโปรแกรม excelเพื่อทาตอนต่อไป (m)
35.
35 =………………………
36.
36 )( 2 1 2 2 2 1 RRMI 23 22 mkg1031.3 )0825.003.0(860.0 2 1 I M=860
g R1=3cm R2=8.25cm = %100 ีค่าจากทฤษฎ ีค่าจากทฤษฎ-งได้ค่าท่ทดลอ
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