Angular Velocity worksheet

1. Angular velocity: 439.82 rad/s

1. Each full turn is 2π radians, so multiply the turns per second (f) by 2π

   $2\times \pi \times 70$$=439.822972\text{\hspace{0.17em}rad/s}$

2. Angular velocity: 3,600 rpm

1. Each full turn is 2π radians, so multiply the turns per second (f) by 2π

   $2\times \pi \times 60$$=376.991118\text{\hspace{0.17em}rad/s}$

2. Change the answer to rpm, the unit you picked: divide by 0.10471975512

   $\frac{376.991118}{0.10471975512}$$=\mathrm{3,600}\text{\hspace{0.17em}rpm}$

3. Angular velocity: 36 °/s

1. Convert the angle to radians, the unit the formula uses (1 ° = 0.0174532925 rad)

   $72\text{\hspace{0.17em}°}\times 0.0174532925$$=1.256637\text{\hspace{0.17em}rad}$

2. Divide the angle turned by the time it took to get the angular velocity (ω)

   $\frac{1.256637}{2}$$=0.628319\text{\hspace{0.17em}rad/s}$

3. Change the answer to °/s, the unit you picked: divide by 0.01745329252

   $\frac{0.628319}{0.01745329252}$$=36\text{\hspace{0.17em}°/s}$

4. Angular velocity: 31.67 °/s

1. Convert the angle to radians, the unit the formula uses (1 ° = 0.0174532925 rad)

   $95\text{\hspace{0.17em}°}\times 0.0174532925$$=1.658063\text{\hspace{0.17em}rad}$

2. Divide the angle turned by the time it took to get the angular velocity (ω)

   $\frac{1.658063}{3}$$=0.552688\text{\hspace{0.17em}rad/s}$

3. Change the answer to °/s, the unit you picked: divide by 0.01745329252

   $\frac{0.552688}{0.01745329252}$$=31.666667\text{\hspace{0.17em}°/s}$

5. Angular velocity: 21,600 °/s

1. Each full turn is 2π radians, so multiply the turns per second (f) by 2π

   $2\times \pi \times 60$$=376.991118\text{\hspace{0.17em}rad/s}$

2. Change the answer to °/s, the unit you picked: divide by 0.01745329252

   $\frac{376.991118}{0.01745329252}$$=\mathrm{21,600}\text{\hspace{0.17em}°/s}$

6. Angular velocity: 35 °/s

1. Convert the angle to radians, the unit the formula uses (1 ° = 0.0174532925 rad)

   $70\text{\hspace{0.17em}°}\times 0.0174532925$$=1.22173\text{\hspace{0.17em}rad}$

2. Divide the angle turned by the time it took to get the angular velocity (ω)

   $\frac{1.22173}{2}$$=0.610865\text{\hspace{0.17em}rad/s}$

3. Change the answer to °/s, the unit you picked: divide by 0.01745329252

   $\frac{0.610865}{0.01745329252}$$=35\text{\hspace{0.17em}°/s}$

7. Angular velocity: 58 rev/s

1. Each full turn is 2π radians, so multiply the turns per second (f) by 2π

   $2\times \pi \times 58$$=364.424748\text{\hspace{0.17em}rad/s}$

2. Change the answer to rev/s, the unit you picked: divide by 6.28318530718

   $\frac{364.424748}{6.28318530718}$$=58\text{\hspace{0.17em}rev/s}$

8. Angular velocity: 222.82 rpm

1. Divide the speed by the radius, because a point's speed grows with its distance from the center

   $\frac{14}{0.6}$$=23.333333\text{\hspace{0.17em}rad/s}$

2. Change the answer to rpm, the unit you picked: divide by 0.10471975512

   $\frac{23.333333}{0.10471975512}$$=222.81692\text{\hspace{0.17em}rpm}$

9. Angular velocity: 120 °/s

1. One full turn (2π radians) takes one period (T), so divide 2π by the period

   $\frac{2\times \pi }{3}$$=2.094395\text{\hspace{0.17em}rad/s}$

2. Change the answer to °/s, the unit you picked: divide by 0.01745329252

   $\frac{2.094395}{0.01745329252}$$=120\text{\hspace{0.17em}°/s}$

10. Angular velocity: 9.17 rpm

1. Convert the angle to radians, the unit the formula uses (1 ° = 0.0174532925 rad)

   $110\text{\hspace{0.17em}°}\times 0.0174532925$$=1.919862\text{\hspace{0.17em}rad}$

2. Divide the angle turned by the time it took to get the angular velocity (ω)

   $\frac{1.919862}{2}$$=0.959931\text{\hspace{0.17em}rad/s}$

3. Change the answer to rpm, the unit you picked: divide by 0.10471975512

   $\frac{0.959931}{0.10471975512}$$=9.166667\text{\hspace{0.17em}rpm}$