Question

A turbine fan in a jet engine has a moment of inertia $2.5kg{m^2}$ about its axis of rotation. Its angular momentum is $40{t^2}$. Find net torque at any instant.
A. $100t$
B. $100{t^2}$
C. $200t$
D. $200{t^2}$

Answer 1

Hint:Firstly, in this question we need to find the torque of the net engine. For that we used the formula of proportionality of the torque to the rate of change of the angular momentum. By putting the values, we can find our solution.

Complete Step by Step Answer:
Torque $\left( \tau \right)$ of the engine be given by $\tau = \dfrac{{dL}}{{dt}}$
where $L$ is the angular momentum
Angular momentum $L = I\omega $ is valid for motion of point particle.
where $I$ is the momentum of inertia and $\omega $ is the orbital angular velocity.
Moment of inertia is the quantity that determines the torque needed for desired angular acceleration about the rotational axis.
We are provided with $I = 2.5kg{m^2}$ $\omega = 40{t^2}$
$\tau = \dfrac{{d\left( {2.5 \times 40{t^2}} \right)}}{{dt}}$
$\therefore\tau = 200t$

Hence, the correct option is C.

Additional information:
Moment of inertia can also be defined as the product of mass of the object and the effective radius which is dependent on a particular axis of rotation. $I = m{k^2}$
where $k$ is the radius of gyration about the axis. Radius of gyration is defined as the radial distance to a point which would have a moment of inertia the same as the body’s actual distribution of mass, if total mass is concentrated there.

Note:Torque is the rotational or twisting effect of a force. Generally, torque on a point particle is defined as, $\tau = F \times r$ where $F$ is the force acting on the particle and $r$ is the particle’s position vector. Torque is a vector quantity. Although force and acceleration are always parallel and directly proportional, torque need not to be parallel and directly proportional to the angular acceleration.