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

Given :

Initial angular velocity = 2 rad/s

Angular acceleration = 3 rad/s²

To Find :

Angular displacement of particle after 4 seconds.

Solution :

❖ Since angular acceleration of particle is said to be constant throughout the motion we can easily apply equation of rotational kinematics to solve this question$.$

Second equation of rotational kinematics is given by

• θ = ωt + 1/2 αt²

» θ denotes angular displacement

» ω denotes initial angular velocity

» t denotes time

» α denotes angular acceleration

By substituting the given values;

➠ θ = (2 × 4) + 1/2 (3 × 4²)

➠ θ = 8 + 1/2 (3 × 16)

➠ θ = 8 + 1/2 (48)

➠ θ = 8 + 24

➠ θ = 32 rad

∴ Angular displacement of the particle after 4 seconds is 32 rad.

Answer 2

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.

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