Question

if initial frequency is 1 rpm and final frequency is 3 rpm it will changes within 20 secs . calculate angular acceleration of a particle .​

Answer 1

Answer:

Given:

Initial angular freq. = 1 rpm

Final angular frequency = 3 rpm

Time taken = 20 sec.

To find:

Angular acceleration

Conversion:

First we shall convert rpm to rad/s

1 rpm = 1 × (2π/60) = π/30 rad/s

3 rpm = 3 × (2π/60) = π/10 rad/s

Calculation:

$\alpha = \dfrac{ \omega2 - \omega1}{t}$

$= > \alpha = \dfrac{ \dfrac{\pi}{10} - \dfrac{\pi}{30} }{20}$

$= > \alpha = \dfrac{2\pi}{30 \times 20}$

$= > \alpha = \dfrac{\pi}{300} \: rad {s}^{ - 2}$

So final answer is :

Angular acceleration = π/300 rad/s²

Answer 2

Answer:

Given:

⇏ If initial frequency is 1 rpm and final frequency is 3 rpm it will changes within 20 seconds.

Find:

⇏ Calculate angular acceleration of a particle.

Note:

⇏ To find the angular acceleration let's change the rmp into rad/s.

⇏ [1 rmp is equal to 1 × 2π/60]

.•. ATQ, 3 rmp is given so if 1 rmp is equal to 2π/60, so now let's find for 3 rmp.

.•. 3 rmp = [3 × 2π/60]

⇏3 × 10 = 60

⇏ π/10

Using the above values for further calculations:

⇏ α (ω2 - ω21)/t

⇏ α = (π/10 - π/30)/20

⇏ α = 2π × (30 × 20)

⇏ α = π/300 rads-²

Therefore, π/300 rads-² is the angular acceleration of a particle.