Question

A body is moving in a circle of radius 100 cm with a time period of 2 s. Find the
acceleration.

Answer 1

$\mathtt{ \huge{ \fbox{Solution :)}}}$

Given ,

• Radius of circle = 100 cm or 0.1 m
• Time period (t) = 2 sec

We know that , angular velocity (ω) is given by

$\large \mathtt{ \fbox{Angular \: velocity (ω) = \frac{2\pi}{t} }}$

Thus ,

ω = (2 × π)/ 2

ω = π

ω = 22/7 rad/sec

We know that , the angular acceleration (α) is given by

$\large \mathtt{ \fbox{α = \frac{ {(linear \: velocity)}^{2} }{radius} }}$

It can be written as ,

$\star \: \large \mathtt{ \fbox{ α = \frac{ {(ω \: \times \: r )}^{2} }{r} }} \\ \\ \star \: \mathtt{\large \fbox{α = {(ω)}^{2} \times r}}$

Thus ,

α = (22/7)² × 0.1

α = 484/490

α = 0.98 rad/sec²

Hence , the angular acceleration is 0.98 rad/sec²

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Answer 2

Explanation:

Given: r = 100cm =0.1m

t=2s

As, accl^n=?

Angular velocity =2 pi/ t

= 2×3.14/2

=3.14 rad /s

Velocity = angular velocity ×radius

=3.14×0.1

= 0.314m/s

Acceleration =v^2/r

=0.314×0.314/0.1

= 98596×10^-5

=0.98596m/s^2

Hope this is helpful for you..