Question

[tex]
{\huge{\underline{\rm{\QUESTION :- }}}} [tex]

Calculate the lenear acceleration of a particle moving in a circle of radius 0.4 m at the instant when its angular velocity is 2 rad/sec and its angular acceleration is 5 rad/ sec^2 .

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Answer 1

Given:

• Radius = r= 0.4m
• Angular velocity = w =2 rad/ sec
• Angular Acceleration a= 5 rad/s²

Need to find:

• Linear acceleration = a= ?

Solution :

We know,

Tangential acceleration = a r

→ Tangential acceleration = 5x0.4 m/s²

→ Tangential Acceleration 2m/s²

Centripetal Acceleration = w²r

→ Centripetal Acceleration = 2x2x0.4 m/s²

→ Centripetal Acceleration = 1.6 m/s²

Net acceleartion:

√Tangential Acceleration²

→ √2²+ 1.6²

→ √4+2.56 m/s²

→ √6.56m/s²

→ 2.6 m/s²

Answer 2

Given:

Radius

$\sf \huge \purple { r= 0.4m}$

Angular velocity = w =2 rad/ sec

Angular Acceleration a= 5 rad/s²

Need to find:

Linear acceleration = a= ?

Solution :

We know,

Tangential acceleration = a r

→ Tangential acceleration = 5x0.4 m/s²

→ Tangential Acceleration 2m/s²

Centripetal Acceleration = w²r

→ Centripetal Acceleration = 2x2x0.4 m/s²

→ Centripetal Acceleration = 1.6 m/s²

Net acceleartion:

√Tangential Acceleration²

→ √2²+ 1.6²

→ √4+2.56 m/s²

→ √6.56m/s²

$\huge \mathfrak \red{→ 2.6 m/s²}$