Question

If my angular velocity slows from 30 Hz to 20 Hz in 72°, what is my deceleration?

Answer 1

Answer:

The deceleration is -7.85x10³ rad/s².

Explanation:

The angular speed (ω) is related to frequency (f) as follows:

$\omega = 2\pi f$

When the frequency is 30 Hz the angular speed is:

$\omega_{i} = 2\pi f = 2\pi*30 Hz = 188.5 rad/s$

Now, when the frequency is 20 Hz the angular speed is:

$\omega_{f} = 2\pi*20 Hz = 125.7 rad/s$

Finally, the angular acceleration (α) can be found using the following equation:

$\omega_{f}^{2} = \omega_{i}^{2} + 2\theta \alpha$

Where:

θ: is the angular displacement = 72°

$\alpha = \frac{\omega_{f}^{2} - \omega_{i}^{2}}{2\theta}$

$\alpha = \frac{(125.7 rad/s)^{2} - (188.5 rad/s)^{2}}{2*72*\frac{2\pi rad}{360}} = -7.85 \cdot 10^{3} rad/s^{2}$        

       

Therefore, the deceleration is -7.85x10³ rad/s².

I hope it helps you!