An object's moment of inertia is 2.0 kg · m2. its angular velocity is increasing at the rate of 4.0 rad/s per second. what is the net torque on the object?

To solve the problem, we can use the equivalent of Newton's second law for rotational motions:
[tex]\tau = I \alpha[/tex]
where
[tex]\tau[/tex] is the net torque acting on the object
I is the moment of inertia of the body
[tex]\alpha[/tex] is the angular acceleration of the object.

Using the data of the problem: [tex]I=2.0 kg \cdot m^2[/tex] and [tex]\alpha=4.0 rad/s^2[/tex], we find the net torque acting on the object:
[tex]\tau=(2.0 kg \cdot m^2)(4.0 rad/s^2)=8.0 N \cdot m[/tex]

johanrusli johanrusli · Answer 2 · 2020-01-11T05:34:54+01:00

The net torque on the object is 8.0 Nm

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Further explanation

Let's recall Net Torque and Moment of Inertia formula on the object as follows:

[tex]\boxed {\Sigma \tau = I \alpha}[/tex]

where:

Στ = net torque ( N.m )

I = moment of inertia ( kg.m² )

α = angular acceleration ( rad/s² )

[tex]\texttt{ }[/tex]

[tex]\boxed { I = M R^2 }[/tex]

where:

I = moment of inertia ( kg.m² )

M = mass of object ( kg )

R = radius of object ( m )

[tex]\texttt{ }[/tex]

Given:

moment of inertia of the object = I = 2.0 kg.m²

angular acceleration = α = 4.0 rad/s²

Asked:

net torque = Στ = ?

Solution:

We could calculate the net torque on the object as follows:

[tex]\Sigma \tau = I \alpha[/tex]

[tex]\Sigma \tau = 2.0 \times 4.0[/tex]

[tex]\Sigma \tau = 8.0 \texttt{ Nm}[/tex]

[tex]\texttt{ }[/tex]

The net torque on the object is 8.0 Nm

[tex]\texttt{ }[/tex]

Learn more

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The Ratio of the Moments of Inertia : https://brainly.com/question/2176655

[tex]\texttt{ }[/tex]

Answer details

Grade: High School

Subject: Physics

Chapter: Rotational Dynamics