Question

By applying a constant torque a wheel is turned 2 revolution in 8 sec. The angular velocity of
wheel after 10 sec from start. (rad/sec)
(1) 4
50
(2) 21
(3) 5
1
solch fler
(4) 5​

Answer 1

Given:

By applying a constant torque a wheel is turned 2 revolution in 8 sec.

To find:

The angular velocity of wheel after 10 sec from start ( in rad/sec) ?

Calculation:

First we need to calculate the angular acceleration :

$\therefore \: \theta = \omega_{0}t + \dfrac{1}{2} \alpha {t}^{2}$

$\implies\: 2 \times 2\pi = (0)t + \dfrac{1}{2} \alpha {(8)}^{2}$

$\implies\: 4\pi = 32\alpha$

$\implies\: \alpha = \dfrac{\pi}{8} \: rad/ {s}^{2}$

Now, let's calculate final angular velocity:

$\therefore \: \omega = \omega_{0} + \alpha t$

$\implies \: \omega = 0 + \dfrac{\pi}{8} \times 10$

$\implies \: \omega = \dfrac{5\pi}{4} \: rad/s$

So, final angular velocity is 5π/4 rad/s.