Question

You’re flying a toy plane on a string, and it’s going around at 20.0 m/sec, 10.0 m from you. If it accelerates to a final velocity of 30.0 m/sec in 80.0 seconds, what is its angular acceleration?

Answer 1

Let's first find the tangential acceleration of the toy plane:

$$a_t=\dfrac{v-v_0}{t}=\dfrac{30\ \dfrac{m}{s}-20\ \dfrac{m}{s}}{80\ s}=0.125\ \dfrac{m}{s^2}.$$

We can find the angular acceleration of the toy plane from the formula:

$$a_t=r\alpha,$$ $$\alpha=\dfrac{a_t}{r}=\dfrac{0.125\ \dfrac{m}{s^2}}{10\ m}=0.0125\ \dfrac{rad}{s^2}.$$