Question

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?

Answer 1

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:

$\boxed {\Sigma \tau = I \alpha}$

where:

Στ = net torque ( N.m )

I = moment of inertia ( kg.m² )

α = angular acceleration ( rad/s² )

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$\boxed { I = M R^2 }$

where:

I = moment of inertia ( kg.m² )

M = mass of object ( kg )

R = radius of object ( m )

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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:

$\Sigma \tau = I \alpha$

$\Sigma \tau = 2.0 \times 4.0$

$\Sigma \tau = 8.0 \texttt{ Nm}$

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The net torque on the object is 8.0 Nm

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Learn more

• Impacts of Gravity : brainly.com/question/5330244
• Effect of Earth’s Gravity on Objects : brainly.com/question/8844454
• The Acceleration Due To Gravity : brainly.com/question/4189441
• Moment of Inertia : brainly.com/question/13796477
• The Ratio of the Moments of Inertia : brainly.com/question/2176655

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Answer details

Grade: High School

Subject: Physics

Chapter: Rotational Dynamics

Answer 2

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

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