Question

A wheel is rotating with angular velocity 2 rad/s. It is subjected to uniform angular acceleration 2.0 rad/
(a) How much angular velocity does the wheel acquire after 10 s?
(b) How many complete revolution it makes in this time interval?

Answer 1

Answer:

Given -

• $\omega$ = 2 rad/s
• $\alpha$ = 2.0 rad/s

$\\ \sf \omega_f = \omega_i + \alpha_t \\ \\ \\ \implies \sf \: \omega_f = 2 + 2(10) \\ \\ \\ \implies \sf \: \omega_f = 22 \: rad.$

Now, we'll find angular velocity using formula -

$\\ \sf \theta = \omega_i \times t + \frac{1}{2} \times \alpha \times {t}^{2}$

Now, by putting the given values in formula -

$\\ \theta = \sf \: 2 \times 10 + \frac{1}{2} \times 2 \times 10 \times 10 \\ \\ \\ \implies \sf \theta = 10 + \frac{1}{2} \times 2 \times 100 \\ \\ \\ \implies \sf \: 20 + 100 \\ \\ \\ \implies \sf \blue{ \theta = 120 \: \: rad}$

Therefore, the angular velocity of the wheel acquires in 10 sec is 120 rad/s.

__________________________

It's total revolution in that time interval -

$\\ \sf \: 120 \: rad \longrightarrow \: \frac{1}{2\pi } \times 100 \\ \\ \\ \implies \sf \: \frac{60}{3.14} \\ \\ \\ \implies \sf{ \underline{ \red{19.09 \: \: revolution.}}}$

Answer 2

I hope its helps us