Question

a constant torque of thousand Newton metre turns A wheel of moment of inertia 200 kilogram per metre square about an Axis through its Centre its angular velocity after 3 seconds​

Answer 1

Answer:

ω = 15 rad / s

Explanation:

tau = 1000 Nm        &         I = 200 kgm²           &           t = 3 s

tau = I α = I ω / t

ω = tau x t / I

ω = 1000 x 3 / 200

ω = 15 rad / s

Answer 2

The angular velocity of the wheel after 3 seconds​ is 15 radian/seconds.

Explanation:

It is given that,

Torque, $\tau=1000\ N-m$

Moment of inertia of the wheel, $I=200\ kg/m^2$

The torque acting on the wheel in case of rotational kinematics is given by :

$\tau=I\times \alpha$

$\alpha =\dfrac{\tau}{I}$

$\alpha =\dfrac{1000}{200}$

$\alpha =5\ rad/s^2$

We need to find the angular velocity after 3 seconds​. It can be calculated using first equation of kinematics as :

$\omega_f=\omega_o+\alpha t$

Initially, $\omega_o=0$

$\omega_f=\alpha t$

$\omega_f=5\times 3$

$\omega_f=15\ rad/s$

So, the angular velocity of the wheel after 3 seconds​ is 15 radian/seconds. Hence, this is the required solution.

Learn more,

Rotational kinematics

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