[b][color=#ff0000]360[/color][/b]

[color=#ff0000][b]6400[/b][/color]

[math]2\pi[/math]

[b][color=#ff0000]4000[br][br][/color][/b]The calculation that we need to do is[br][br][math]\frac{225}{360}\times6400=4000[/math] (Remember, divide by a whole revolution in the old units (360), times by a whole revolution in the new units (6400))

[math]\frac{7\pi}{4}rads[/math] or 5.50 rads[br][br]The calculation we need to do is[br][br][math]\frac{315}{360}\times2\pi=\frac{7\pi}{4}[/math] (Remember, divide by a whole revolution in the old units (360), times by a whole revolution in the new units ([math]2\pi[/math]))

[math]\frac{9}{16}[/math][br][br]There are 6400 mils in a whole revolution, and we have an angle of 3600 mils. Therefore as a fraction of a revolution that is[br][br][math]\frac{3600}{6400}=\frac{9}{16}[/math]

[b][color=#ff0000]112.5[sup]o[/sup][/color][/b][br][br]The calculation we need to do is[br][br][math]\frac{2000}{6400}\times360=112.5[/math] (Remember, divide by a whole revolution in the old units (6400), times by a whole revolution in the new units (360))

[b][color=#ff0000]209.4 rads/sec[br][br][/color][/b]Method 1:[br][br][math]2000\times\frac{2\pi}{60}=209.439510...\approx209.4[/math] ([math]\times\frac{2\pi}{60}[/math] is the conversion you should remember)[br][br]Method 2:[br][br]First divide 2000 rpm by 60, as this now gives us revs/sec.[br][br][math]2000\div60=33.333...[/math][br][br]Then multiply by [math]2\pi[/math] as one revolution is [math]2\pi[/math] radians and so we now get rads/sec.[br][br][math]33.333...\times2\pi=209.439510...\approx209.4[/math][br][br]The second method is useful if you can't remember whether the [math]2\pi[/math] or the [math]60[/math] goes on the top of the fraction in method 1.

[b][color=#ff0000]1909.9 rads/sec[br][br][/color][/b]Method 1:[br][br][math]200\times\frac{60}{2\pi}=1909.859317...\approx1909.9[/math] ([math]\times\frac{60}{2\pi}[/math] is the conversion you should remember)[br][br]Method 2:[br][br]First multiply 200 rads/sec by 60, as this now gives us rads/min.[br][br][math]200\times60=12000[/math][br][br]Then divide by [math]2\pi[/math] as one revolution is [math]2\pi[/math] radians and so we now get rads/sec.[br][br][math]12000\div2\pi=1909.859317...\approx1909.9[/math][br][br]The second method is useful if you can't remember whether the [math]2\pi[/math] or the [math]60[/math] goes on the top of the fraction in method 1.

[color=#ff0000][b]0.8 of a rev[/b][/color][br][br]Convert them all to the same measure. Revs is easiest.[br][br][math]\frac{250}{360}=0.694444...revs[/math][br][br][math]\frac{5000}{6400}=0.78125revs[/math][br][br][math]\frac{5}{2\pi}=0.795774...revs[/math][br][br]So 0.8 of a rev is the largest of them.[br][br]Alternatively, you could convert them all to degrees, or any other measure.