The rotor of an electric motor has rotational inertia Im = 7.17 x 10-3 kg·m2 about its central axis. The motor is used to change the orientation of the space probe in which it is mounted. The motor axis is mounted along the central axis of the probe; the probe has rotational inertia Ip = 6.84 kg·m2 about this axis. Calculate the number of revolutions of the rotor required to turn the probe through 44.1° about its central axis.

Question

Arnav Lozano

Mathematics

30 October, 19:49

The rotor of an electric motor has rotational inertia Im = 7.17 x 10-3 kg·m2 about its central axis. The motor is used to change the orientation of the space probe in which it is mounted. The motor axis is mounted along the central axis of the probe; the probe has rotational inertia Ip = 6.84 kg·m2 about this axis. Calculate the number of revolutions of the rotor required to turn the probe through 44.1° about its central axis.

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Imani Gallagher · Answer 1

the number of revolutions of the rotor required to turn the probe through 44.1° about its central axis is approximately 117 revolution.

Step-by-step explanation:

From the conservation of angular momentum of the motor

Ip * theta p = Im * theta m

Where IP = 6.84 is the rotational inertia of the probe along it central axis

Theta p = 44.1°, Im = 7.17 * 10^-3 is the rotational inertia of the electric motor about it central axis.

Ip * theta p = Im * theta m

6.84 * 44.1 = 0.00717 * theta m

301.644 = 0.00717 * theta m

Theta m = 301.644 / 0.00717

= 42,070.3°

Number of revolution = 42,070.3°/360

= 117 revolution