Question

Avon starts from rest and attains a angular velocity of 20 m per second after being uniformly accelerated for 10 seconds the total angle in radian through which it has started in 10 seconds is

Answer 1

Answer:

Given:

Initial angular Velocity = 0 rad/s

Final angular Velocity = 20 rad/s

Time taken = 10 seconds

To find:

Total angular displacement

Calculation:

Let initial Angular velocity be denoted by "ω".

angular acceleration (α)

α = (final ang.vel. - initial ang.vel.)/time

=> α = (20 - 0)/10

=> α = 2 rad/s² .........(1)

Now angular displacement (θ)

θ = ωt + ½αt²

=> θ = (0 × t) + ½ × 2 × 10²

=> θ = 100 rad.

So the final answer is

$\huge{\boxed{θ \: = 100 \: radians}}$

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

$\tt {\blue{Given}} \begin{cases} \sf{\green{Intial \: Angular \: Velocity \: (\omega _{0}) \: = \: 0 \: rad/s}} \\ \sf{\orange{Final \: Angular \: Velocity \: (\omega) \: = \: 20 \: rad/s}} \\ \sf{\pink{Time \: Period \: (T) \: = \: 10 \: s}} \end{cases}$

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✪ To Find :

Angle of acceleration

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✪ Solution :

We need to find angular acceleration

$\Large{\underline{\boxed{\gray{\sf{\alpha \: = \: \frac{\omega \: - \: \omega _{0}}{Time}}}}}}$

Put Values

⇒α = (20 - 0)/10

⇒α = 20/10

⇒α = 2

$\Large{\boxed{\sf{\purple{\alpha \: = \: 2 \: rad /s^2}}}}$

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We have formula for Theta :

$\Large{\underline{\boxed{\green {\sf{\theta \: = \: \omega t \: + \: \frac{1}{2} \alpha t^2}}}}}$

Put Values

⇒θ = (0)(10) + ½ (2)(10)²

⇒θ = 0 + ½ 2(100)

⇒θ = ½ * 200

⇒θ = 100

$\large{\boxed{\red{\sf{\theta \: = \: 100 \: rad}}}}$

∴ Angle in radians is 100 rad

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