Question

(ii) calculate the linear acceleration of a particle moving in a circle of radius
0.4 m at the instant when its angular velocity is 2 rad/s and its acceleration is
5 rad/s?​

Answer 1

Given:

• Radius = r = 0.4m
• Angular velocity = ω = 2 rad/ sec
• Angular Acceleration = α= 5 rad/${s}^{2}$

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Need to find:

• Linear acceleration = a =?

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Solution :

We know,

Tangential acceleration = α r

⟹ Tangential acceleration = 5×0.4 m/${s}^{2}$

⟹ Tangential Acceleration = 2m/${s}^{2}$

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We know

Centripetal Acceleration = ${ \omega}^{2} r$

⟹ Centripetal Acceleration = 2×2×0.4 m/${s}^{2}$

⟹ Centripetal Acceleration = 1.6 m/${s}^{2}$

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Net acceleartion:

$= \sqrt{ {Tangential\:Acceleration }^{2} + {Centripetal \: Acceleration}^{2} }$

$= \sqrt{ {2}^{2} + {1.6}^{2} }$

$= \sqrt{4 + 2.56} \: m/ {s}^{2}$

$= \sqrt{6.56} m/ {s}^{2}$

${\red{\bold{\boxed{ \approx \: 2.6 \: m /{s}^{2}}}}}$

Answer 2

Answer:

0.64 m/s² and 2 m/s²

Explanation:

When ω = 2 rad/s

α = ω² × r

α = 2² × 0.4

α = 4 × 0.4

α = 1.6 m/s²

Therefore, a = α × r

                  a = 1.6 × 0.4

                  a = 0.64 m/s²

When α = 5 rad/s²

a = α × r

a = 5 × 0.4

a = 2 m/s²