Question

A spacecraft at rest has moment of inertia of 100 kg-m^2 about an axis of interest. If a 1 newton thruster with a 1 meter moment arm is fired orthogonal to the axis of interest for 1 minute, how far has the vehicle rotated when the firing is complete?

Answer 1

18 radians

Step-by-step explanation:

The computation is shown below:

As we know that

Torque = Force × Moment arm

= 1N × 1M

= 1N-M

Torque =
`I\alpha`

`\alpha = (torque)/(I)\\\\= (1)/(100)\\\\= 0.01 rad/s^2`

Now

`\theta = w_ot + (1)/(2) \alpha t^2\\\\w_o = 0\\\\\theta = 0 * 60 + (1)/(2) * 0.01 * 60^2\\\\= 18\ radians`

Here t = 1 minutes = 60 seconds