Question

If a 32.0Nmtorque on a wheel causes angular acceleration 25.0rad/s², what is the wheel’s rotational inertia?

Short answer

Rotational inertia of the wheel is 1.28kg.m² .

Step-by-step solution

Understanding the given information

The torque is, $\tau =32N.m$.

The acceleration is, $\alpha =25.0rad/s^2$.

Concept and formula used in the given question

You know the torque is nothing but the product of moment of inertia and angular acceleration. This is given by Newton’s second law for rotation. When a wheel is rotating in a direction, it may have its own angular acceleration as well as inertia. From this, you can calculate torque applied on a wheel. In this problem, the torque is given but inertia has to be calculated. The formulas are stated below.

$\mathit{\tau }\mathbf{=}\mathit{l}\mathit{\alpha }$

Calculation for the wheel’s rotational inertia

Calculating rotational inertia of wheel by using above formula,

$$\begin{gathered} \tau =l\alpha \\ l=\frac{\tau }{\alpha } \end{gathered}$$

Substitute all the value in the above equation

$\begin{array}{rcl}l& =& \frac{32N.m}{25.0rad/s^2}\\ & =& 1.28kg.m^2\end{array}$

Hence the rotational inertia is, 1.28kg.m² .