Question

A wheel of radius 1.5m is rotating at a constant angular acceleration of 10 rad/s sq. .Its angularbspeed is [60/π ]rpm .What will be its angular speed and angukar displacement at t=2.0 s?


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Answer 1

Hello Mate,

Here is your answer,

Given:

• Radius of wheel = 1.5 meters

• Angular acceleration of wheel =$10 \: \: rad {s}^{ - 2}$
• Angular speed of wheel = $\frac{60}{\pi} \: rpm$
• Time = 2.0 seconds

To find:

• Angular speed and displacement of wheel at time = 2 seconds

Formulas Used:

• $w = w_{0} + at$
• $\alpha = \frac{ {w}^{2} + { w_{0}}^{2} }{2a}$

Solution:

We Know,

$\frac{60}{\pi} \: rpm \\ \\ = \frac{ \frac{60}{\pi} \times 2\pi}{60} rad \: {s}^{ - 1} \\ \\ = 2 \: rad \: {s}^{ - 1}$

Now,

$w = w_{0} + at$

$w = 2 + 10(2) \\ \\ w = 22 \: rad \: \: {s}^{ - 1}$

So the Angular speed for t = 2 secs is$22 \: rad \: {s}^{ - 1}$

Now finding Angular displacement,

$\alpha = \frac{ {w}^{2} - { w_{0}}^{2} }{2a} \\ \\ = \frac{ {22}^{2} + {2}^{2} }{2 \times 10} \\ \\ = \frac{480}{20} \\ \\ = 24 \: rad$

The Angular displacement covered by wheel after 2 seconds is 24 rad.

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