Question

A partical is rotating with a constant angular acceleration on a circular track. If its angular velocity changes from 20pi to 40 pi

Answer 1

Answer:

The radius of the circle is r=20πm

Explanation:

Answer 2

Given:

Initial angular velocity (ω₀) = 20π

Final angular velocity (ω) = 40π

Time taken (t) = 10 s

To find:

No of rotations made by the body.

Solution:

Step 1

We have been given that the particle is moving with a uniform angular acceleration,

Hence,

The angular acceleration will be,

$\alpha =\frac{(w_{t} )-(w_{0}) }{t}$

Substituting the values, we get

$\alpha =$ ($40$π $-20$π) /10

$\alpha =2$π $rad/s^{2}$

This means, that the particle is making a uniform acceleration of $2$π $rad/s^{2}$.

Step 2

Hence, the angular distance that the particle will travel in 10 s with this angular acceleration will be

θ $= w_{0} t + \frac{1}{2} at^{2}$

Substituting the given values, we get,

θ $=20$π$(10)+$ $(0.5)$$2$π$(10)^{2}$  

Hence,

θ $=200$π $+ 300$π

θ $=300$π

Hence, the distance traveled by the particle in 10 s is $300$π.

Step 3

We know, in circular motion, when a cycle or circle is completed travelling, the distance covered is $360^{o}$ or $2$π.  

Hence, the no of cycles made while travelling $300$π will be

No of cycles $=300$π $/$$2$π

                     $= 150$

Final answer:

Hence, the number of completes cycles covered by the particle while travelling $300$π $is$ $150$.

Although your question is incomplete, you might be referring to the question below.

A particle rotates with a uniform angular acceleration. Its angular velocity increases from 20π m/s to 40π m/s in 10 seconds. How many rotations did it make in this period.