Question

Angular speed of a particle increases from 2rads to 4 rads across any two diametrically opposite positions. Its angular acceleration will be?
A) 6 rad s?
6
-rad s-2
rad 3
rad s-2
6
Di rad s-2​

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

Answer:

Hello mate

Step-by-step explanation:

Angular acceleration is the simply rate of change of angular velocity.

α=dωdt=ωf−ωit

This is the basic formula in Rotational motion. There are also other basic formulas in Rotational motion which are very similar to linear motion. We simply have to draw few analogies and change one form into another like changing linear displacement S to Angular Displacement θ amongst other things.

So the other equations of Rotational motions are

θ=ωit+(1/2)αt2

ω2f=ω2i+2αθ

In this example we can use the last equation, as we know angular displament(θ) when the particle goes from one pole to diagrammatically opposite pole is just π.

Therefore

α=ω2f−ω2i2θ=16−42π=6π rad s−2

Hence , the angular displacement will be 4 s is to 32 rad