Question

A plane's propeller has a rotational inertia of 2.0kg * m ^ 2 After a clockwise torque of 4.0Nm was applied to the propeller for 4.0s, the propeller has a clockwise angular speed of 24 * (rad)/s What was the initial angular momenturn of the propeller before the torque was applied ?

Answer 1

The initial angular momentum of the propeller before the torque was applied will be 32 kg m²/s.

What is torque?

Torque is the force's twisting action about the axis of rotation. Torque is the term used to describe the instant of force. It is the rotational equivalent of force. Torque is a force that acts in a turn or twist.

The amount of torque is equal to force multiplied by the perpendicular distance between the point of application of force and the axis of rotation.

The given data in the problem is;

The rotational inertia is,I  = 2.0 kg m²

The clockwise torque is, T = 4.0Nm

The time period is,t= 4.0s,

The angular speed is,ω= 24 * (rad)/s

The initial angular momentum of the propeller is,I₀

The angular acceleration is found by the relation;

$\rm \tau = I \times \alpha \\\\ \alpha =\frac{\tau}{i} \\\\ \alpha =\frac{4.0}{2.0} \\\\ \alpha= 2.0 \ rad/sec^2$

The initial angular velocity is found as;

$\rm \omega_f = \omega_0 + \alpha t \\\\ \omega_0 = \omega_f -\alpha t \\\\ \omega_0 =24 -[(-2.0)\times 4.0)] \\\\ \omega_0 = 16 \ rad/sec$

The initial angular momentum of the propeller is found as;

$\rm L_0 = I \omega_0 \\\\ L_0 = 20 \times (1.6) \\\\ I_0 = -32 \ kgm^2/s$

Hence,the initial angular momentum will be 32 kg m²/s.

To learn more about the torque, refer to the link;

brainly.com/question/6855614

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