A small grinding wheel has a moment of inertia of 4.0×10−5 kg⋅m2 . What net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2 ?

The relationship between angular acceleration, net torque and moment of inertia for rotational motion is similar to the Newton's Second Law for linear motion ([tex]F=ma[/tex]):

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

where

[tex]\tau[/tex] is the net torque

I is the moment of inertia

[tex]\alpha[/tex] is the angular acceleration

In this problem, we have:

[tex]I=4.0\cdot 10^{-5} kg m^2[/tex] is the moment of inertia

[tex]\alpha = 150 rad/s^2[/tex] is the angular acceleration

Substituting numbers into the equation, we find the net torque that should be applied:

[tex]\tau=(4.0\cdot 10^{-5} kg m^2)(150 rad/s^2)=0.006 N\cdot m[/tex]

asuwafohjames asuwafohjames · Answer 2 · 2022-04-01T11:47:41+02:00

The torque applied to the wheel is 0.006 Nm.

What is torque?

Torque can be defined as the force that can cause an object to rotate about its axies.

To calculate the net torque applied to the wheel, we use the formula below

Formula:

τ = Iα........... Equation 1

Where:

τ = torque applied to the wheel
I = moment of initial
α = angular acceleration

From the question,

Given:

I = 4.0×10⁻⁵ kgm²
α = 150 rad/s²

Substitute these values into equation 1

τ = (4.0×10⁻⁵)(150)
τ = 0.006 Nm

Hence, The torque applied to the wheel is 0.006 Nm.

Learn more about torque here: https://brainly.com/question/20691242