Question

A particle lerforming circular motion with angular speed 4rad/ s in a circle of radius 1m then find:

Linesr speed, Angular acceleation, tangential acceleration

Answer 1

Correct question:

A particle performing circular motion with angular speed 4rad/sec in a circle of radius 1m then find:

• Linear speed,
• Angular acceleation and
• Tangential acceleration

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Given:

• Angular speed = ω = 4 rad/sec
• Radius = r =1m

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Need to find:

• Linear speed = v =?
• Angular speed = α = ?
• Tangential acceleration = ${A}_{T}$=?

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Solution:

We know,

v= rω

→ v = 1 × 4m/s

→ v= 4 m/s

∴Linear speed is 4 m/s.

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we know,

$\alpha = \dfrac{d \: \omega}{dt}$

$\implies \: \alpha = \dfrac{d4}{dt}$

Differentiation of a constant term is always equal to 0.

$\implies \: \alpha = 0 rad/{sec}^{2}$

∴ Angular acceleration = 0 rad/ $s^{2}$

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Tangential acceleartion:

${A}_{T} = \dfrac{dv}{dt}$

$\implies \: {A}_{T} = \dfrac{d4}{dt}$

$\implies {A}_{T} = 0 rad/ s^{2}$

∴ Tangential acceleration = 0 rad/ $s^{2}$