Question

a particle is in circular motion with an acceleration alpha = 0.2 rad s-2
a) what is the angular displacement made by particle after 5 sec
b)what is the angular velocity at t =5s ? (assume the initial angular velocity is zero)​

Answer 1

Answer:

ANSWER

Given that Angular acceleration of the particle = α=0.2rad/s

2

Using Ist equation of motion for circular motion we get

ω=ω

0

+αt

Since particle is at rest initially ∴ω

0

=0

⟹ω=αt=0.2×10=2rad/s

Answer 2

Given:

• Initial angular velocity = 0 rad/s
• angular acceleration = 0.2 rad/s².

To find:

• Angular displacement made by the particle after 5 seconds ?

• Angular velocity at 5 seconds ?

Calculation:

The general equation of angular displacement as per Rotational Kinematics:

$\theta = \omega t + \dfrac{1}{2} \alpha {t}^{2}$

$\implies \theta = (0)5 + \dfrac{1}{2} (0.2) {(5)}^{2}$

$\implies \theta = 0.1 \times 25$

$\implies \theta =2.5 \: rad$

So, angular displacement is 2.5 radian.

Now, angular velocity will be :

$\omega_{2} = \omega + \alpha t$

$\implies \omega_{2} = 0 + (0.2 \times 5)$

$\implies \omega_{2} = 1 \: rad/s$

So, angular velocity after 5 seconds is 1 rad/sec.