Mbadala wa RPM kuwa rad/s

Fomula za Ubadilishaji

From	To rad/s	To RPM
1 RPM	π/30 ≈ 0.10472	1
1 rad/s	1	30/π ≈ 9.5493
1 deg/s	π/180 ≈ 0.01745	1/6 ≈ 0.1667
1 rev/s	2π ≈ 6.2832	60
1 Hz	2π ≈ 6.2832	60

Kasi za Kawaida za Mota

Poles	50 Hz Sync	50 Hz Typical	60 Hz Sync	rad/s (50 Hz)
2	3000	2940	3600	314.2
4	1500	1460	1800	157.1
6	1000	970	1200	104.7
8	750	720	900	78.5

Kasi ya Angular katika Uhandisi

Kasi ya angular ni msingi katika mahesabu ya mashine zinazozunguka:

• Kuongeza kasi kwa mzunguko (centripetal): a = ω² × r
• Nguvu ya usawa mbaya (unbalance force): F = m × e × ω²
• Uhusiano wa nguvu ya kuzungusha na nguvu ya mwendo: P = T × ω (where P in watts, T in Nm, ω in rad/s)
• Kasi ya angular ya mwendo: L = I × ω
• Nishati ya kinetic: KE = ½ × I × ω²
• Frequency: f = ω / (2π)

Ubadilishaji wa Haraka wa Kiakili

RPM	rad/s (approx)	Hz	Typical Use
60	6.28	1	Slow agitators
300	31.4	5	Slow pumps
750	78.5	12.5	Motors za nguzo 8 (50 Hz)
1000	104.7	16.7	Motors za nguzo 6 (50 Hz)
1500	157.1	25	Motors za nguzo 4 (50 Hz)
3000	314.2	50	Motors za nguzo 2 (50 Hz)
3600	377.0	60	Motors za nguzo 2 (60 Hz)
10000	1047	166.7	Turbochargers
50000	5236	833	Vichimbio vya meno, mikrotabini

Kidokezo: Kariri π/30

The conversion factor from RPM to rad/s is π/30 ≈ 0.10472. So:

• 1000 RPM × 0.10472 ≈ 104.7 rad/s
• 1500 RPM × 0.10472 ≈ 157.1 rad/s
• 3000 RPM × 0.10472 ≈ 314.2 rad/s (≈ 100π)