A disc which is at rest started to spin about a stationary axis- The angular acceleration of the disc is given by - - 2 - rad-s- where - is the angle of rotation of disc from its initial position- Which of the following graphs correctly represents the variation of angular velocity with respect to - -

Given α = 2θ nbsp; We know α=dωdt=dωdθ×dθdt ⇒ nbsp;ωdωdθ = 2 θ ⇒ω dω = 2θ d θ Integrating on both sides, ∫_0^ωω dω = ∫_0^θ 2 θ d θ ⇒ω^22 = 2 θ^22 ⇒ w = √(2) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Radial & Tangential Acceleration for Non Uniform Circular Motion

A disc which ...

Question

A disc which is at rest started to spin about a stationary axis. The angular acceleration of the disc is given by $α = 2 θ r a d / s$ , where $θ$ is the angle of rotation of disc from its initial position. Which of the following graphs correctly represents the variation of angular velocity with respect to ' $θ$ ' ?

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
Given $α = 2 θ$
We know $α = \frac{d ω}{d t} = \frac{d ω}{d θ} \times \frac{d θ}{d t}$
$\Rightarrow ω \frac{d ω}{d θ} = 2 θ$
$\Rightarrow ω d ω = 2 θ d θ$
Integrating on both sides,
$\int_{0}^{ω} ω d ω = \int_{0}^{θ} 2 θ d θ$
$\Rightarrow \frac{ω^{2}}{2} = 2 \frac{θ^{2}}{2}$
$\Rightarrow w = \sqrt{2} θ$
Therefore, graph is a straight line passing through origin. (option b)

Suggest Corrections

Similar questions

Q. A solid body starts from rest. Angular acceleration of the body spinning about a stationary axis is given by

α = 2 cos θ

(in

r a d / s^{2}

) where

θ

is the angle of rotation from initial position. Then which of the following graphs correctly represents the variation of angular velocity with respect to

θ

Q. Angular acceleration of a circular disc which is initially at rest, about a stationary axis is

α = 8 cos 2 t

(in

{rad/s}^{2}

). Which of the following graphs correctly represents the variation of angular velocity with respect to time ?

Q. If angular velocity of a disc depends an angle rotated

θ

ω = θ^{2} + 2 θ

, then its angular acceleration

α

θ = 1 rad

A disc rotates about a fixed axis. Its angular velocity $ω$ varies with time according to the equation $ω = at + b$ . Initially at t = 0 its angular velocity is 1.0 rad/s and angular position is 2 rad; at the instant t= 2s angular velocity is 5.0 rad/s. Determine angular position $θ$ and angular acceleration when t = 4s.

Q. If angular velocity of a disc depends an angle rotated

θ

ω = θ^{2} + 2 θ

, then its angular acceleration

α

θ = 1 rad

Join BYJU'S Learning Program

The correct option is B Given α=2θ We know α=dωdt=dωdθ×dθdt ⇒ωdωdθ=2θ ⇒ωdω=2θdθ Integrating on both sides, ∫ω0ωdω=∫θ02θdθ ⇒ω22=2θ22 ⇒w=√2θ Therefore, graph is a straight line passing through origin. (option b)