Question

inetial angular speed of a particle is 2 rad s-1 and contant angular acceleration is 3 rad rad s-2 then after 4 s it's angular displacement is .... rad​

Answer 1

Answer :

• Angular displacement of the particle after 4 s, θₜ = 32 rad

Explanation :

Given :

• Initial angular speed of the particle, ω₀ = 2 rad/s
• Angular acceleration of the particle, α = 3 rad/s²
• Time, t = 4 s

To find :

• Angular displacement of the particle after 4 s, θₜ = ?

Knowledge required :

• Equation for angular displacement :

⠀⠀⠀⠀⠀⠀⠀⠀⠀θₜ = ω₀t + ½αt²⠀

[Where : θₜ = Angular displacement of the particle, ω₀ = Initial angular speed of the particle, α = Angular acceleration of the particle and t = Time taken]

Solution :

To find the angular displacement of the particle after 4 s :

By using the formula for angular displacement of a particle and substituting the values in it, we get :

⠀⠀=> θₜ = ω₀t + ½αt²

⠀⠀=> θ₄ = 2 × 4 + ½ × 3 × 4²

⠀⠀=> θ₄ = 8 + ½ × 3 × 16

⠀⠀=> θ₄ = 8 + 24

⠀⠀=> θ₄ = 32

⠀⠀⠀⠀⠀∴ θ₄ = 32 rad

Hence, the angular displacement of the particle after 4 s is 32 rad.

Answer 2

$\huge{\underline{\mathtt{\red{H}\pink{E}\green{L}\blue{L}\orange{O}}}}$

$\pink{To \: find \: the \: angular \: displacement \: of \: the \: particle \: after \: 4 s :}$

By using the formula for angular displacement of a particle and substituting the values in it, we get :

⠀⠀=> θₜ = ω₀t + ½αt²

⠀⠀=> θ₄ = 2 × 4 + ½ × 3 × 4²

⠀⠀=> θ₄ = 8 + ½ × 3 × 16

⠀⠀=> θ₄ = 8 + 24

⠀⠀=> θ₄ = 32

⠀⠀⠀⠀⠀∴ θ₄ = 32 rad

$\purple{Hence, the \: angular \: displacement \: of \: the \: particle \: after \: 4 \: s \: is \: 32 \: rad.}$

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