Question

A wheel rotates for 5 seconds with constant angular acceleration and describes during this time 100 radians. it then rotates with constant angular velocity and during the next 5 seconds describes 80 radians. find initial angular velocity and angular acceleration.

Answer 1

Initial angular velocity = 24 rad/s

and  angular acceleration = 1.6 rad/s²

Given: A wheel rotates for 5 seconds with constant angular acceleration and covers a distance of 100 radians.

Then, it rotates with constant angular velocity and during the next 5 seconds describes 80 radians.

To Find: initial angular velocity and angular acceleration.

Solution:

The question can be solved using Newton's laws of motion,

1.     θ = ωt + 1/2 αt²     [ where, θ = distance, ω = initial angular velocity]

2.     ωf = ω + αt    [ where, ωf = final angular velocity, α = acceleration ]

It it said that the wheel rotates with constant angular velocity, thus, angular acceleration for this part is zero.

θ = 80, t = 5 s

   θ = ωt + 1/2 αt²        

⇒ 80 = ω × 5                        [ as angular acceleration is zero ]

⇒ ω = 16 rad/s

Now, it is said that the wheel covers 100 radians in 5 s with constant angular acceleration, so here;

ωf = 16 rad/s, t = 5 s, θ = 100 radians

   θ = ωt + 1/2 αt²

⇒ 100 = 5ω - 1/2 α × 25                     [ due to deceleration ]

⇒ 2ω - 5α = 40                                 ..... (1)

   ωf = ω + αt  

⇒ 16 = ω - 5α                                    ......(2)  [ due to deceleration ]

Solving equations (1) and (2), we get,

ω = 24 rad/s

α = 1.6 rad/s²

Hence, initial angular velocity = 24 rad/s

and  angular acceleration = 1.6 rad/s²

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Answer 2

Answer:

The answer $\alpha =-1.6rad/s^{2}$

Constant angular acceleration (CAV), which can also be used to describe the writing speed of video recording discs, is a qualification for any disc that contains information. In contrast to constant constant speed, a drive or disc in CAV mode provides a steady angular velocity (CLV).

Explanation:

The angular velocity, which is frequently denoted by the symbol and stated in radians per second per second, is the rate at which the angular velocity changes over time. The rate at which the angular momentum is shifting is known as the angular acceleration. We could state that the angular velocity is constant if the Ferris wheel accelerates at a regular speed.

Given that the wheel rotates for 5 seconds while accelerating at a constant angle, we obtain

θ  = ω + ω₀/2.t

100  = ω + ω₀/2(5)

ω+ω₀ = 40

Knowing that it would continue to spin at a fixed angle for the following t = 5 s, we now have

θ = ωt

80 = ω(5)

ω = 16 rad/s

now we have

16+ω₀ = 40

ω₀ = 24 rad/s

Currently, angular acceleration is stated as

α  = ω + ω₀/t  

α  16 − 24/5  

α = -1.6 rad/s^2

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