Question

A rod of length 20 cm has two beads attached to its ends. The rod with beads starts rotating from rest. If the beads are to have a tangential speed of 20 m/s in 7 s, what is the angular acceleration of the rod to achieve this?

Answer 1

Answer:

$\alpha=28.57\frac{rad}{s^2}$

Explanation:

We use the following rotational kinematic equation to calculate the angular acceleration of the rod:

$\omega_f=\omega_0+\alpha t$

Here $\omega_f$ is the final angular speed, $\omega_0$ is the initial angular speed and $\alpha$ is the angular acceleration. The rod starts rotating from rest ($\omega_0=0$):

$\alpha=\frac{\omega_f}{t}(1)$

Recall that the angular speed is defined in function of the tangential speed (v) and the radius (r) of the circular motion:

$w_f=\frac{v_f}{r}(2)$

In this case the radius is given by $r=\frac{20*10^{-2}m}{2}=0.1m$. Replacing (2) in (1):

$\alpha=\frac{v_f}{rt}\\\alpha=\frac{20\frac{m}{s}}{(0.1m)7s}\\\alpha=28.57\frac{rad}{s^2}$