Answer:
The number of revolutions of the rotor required to turn the probe is 118 revolutions
Explanation:
Given;
rotational inertia of the electric motor, Im = 4.36 x 10⁻³ kg·m²
rotational inertia of the probe, Ip = 6.07 kg·m²
the angular position of the probe, θ = 30.6°
From the principle of conservation of angular momentum;
[tex]I_m \omega _m = I_p \omega _p \\\\Also;\\\\I_m \theta _m = I_p \theta _p[/tex]
where;
[tex]\omega _m[/tex] is the angular velocity of the electric motor
[tex]\omega _p[/tex] is the angular velocity of the probe
[tex]\theta _m[/tex] is the angular position of the electric motor
[tex]\theta _p[/tex] is the angular position of the probe
[tex]\theta _m = \frac{I_p \theta_p}{I_m} \\\\\theta _m = \frac{6.07* 30.6^o}{4.36*10^{-3}} = 42601.4^o[/tex]
360° = One revolution
42601.4° = ?
Divide 42601.4° by 360°
= 118 revolutions
Therefore, the number of revolutions of the rotor required to turn the probe is 118 revolutions