Question

The product of moment of inertia and angular acceleration is:
(A) force
(B) torque
(C) angular momentum
(D) rotational kinetic energy

Answer 1

The SI unit of the moment of the inertia and the SI unit of the angular acceleration is multiplied, then the resultant SI unit is checked with the SI unit of the parameters which are given in the option, then the solution can be determined.

Complete step by step answer:
The moment of inertia is equal to the angular momentum is divided by the angular velocity, then the moment of inertia is written as,
$I = \dfrac{L}{\omega }$
Where, $I$ is the moment of the inertia, $L$ is the angular momentum and $\omega$ is the angular velocity.
So, the SI unit of the moment of inertia is determined by dividing the SI unit of the angular momentum and the SI unit of the angular velocity. Then,
$I = \dfrac{{\left( {\dfrac{{kg{m^2}}}{s}} \right)}}{{\left( {\dfrac{{rad}}{s}} \right)}}$
By rearranging the terms in the above equation, then the above equation is written as,
$I = \dfrac{{kg{m^2}}}{s} \times \dfrac{s}{{rad}}\,.....................\left( 1 \right)$
Now the SI unit of the angular acceleration is given by,
$\alpha = \dfrac{{rad}}{{{s^2}}}\,................\left( 2 \right)$
In the question it is given that the product of the moment of inertia and the angular acceleration, then by multiplying the equation (1) and equation (2), then
$\Rightarrow \dfrac{{kg{m^2}}}{s} \times \dfrac{s}{{rad}} \times \dfrac{{rad}}{{{s^2}}}$
By cancelling the same terms in the above equation, then the above equation is written as,
$\Rightarrow \dfrac{{kg{m^2}}}{{{s^2}}}$
In the above equation the terms $\dfrac{{kgm}}{{{s^2}}}$, is also written as newton $N$, then the above equation is written as,
$\Rightarrow Nm$
By comparing this unit with the option which is given in the question, the unit of the torque is matched with the above equation.

Hence, the option (B) is the correct answer.

Note: The unit of the torque is $Nm$, this the final answer so the answer is determined as the torque. In physics, there is a statement like the torque in the rotating substance is equal to the product of the moment of inertia and the angular acceleration.