Question

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 ?

Answer 1

Answer:

0.006 Nm

Explanation:

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 ($F=ma$):

$\tau = I\alpha$

where

$\tau$ is the net torque

I is the moment of inertia

$\alpha$ is the angular acceleration

In this problem, we have:

$I=4.0\cdot 10^{-5} kg m^2$ is the moment of inertia

$\alpha = 150 rad/s^2$ is the angular acceleration

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

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