Question

A nano-satellite has the shape of a disk of radius 0.80 m and mass 8.50 kg.
The satellite has four navigation rockets equally spaced along its edge. Two
navigation rockets on opposite sides of the disk fire in opposite directions
to spin up the satellite from zero angular velocity to 14.5 radians/s in 30.0
seconds. If the rockets each exert their force tangent to the edge of the
satellite (the angle theta between the force and the radial line is 90
degrees), what was is the force of EACH rocket, assuming they exert the
same magnitude force on the satellite?

Answer 1

Answer:

Explanation:

moment of inertia of satellite I = 1/2 m R²

m is mass and R is radius of the disc

I = 0.5 x 8.5 x 0.8²

= 2.72 kg m²

angular acceleration α = change in angular velocity / time

α = (14.5 - 0) / 30

α = .48333

Let force of each rocket = F

torque created by one rocket = F x R

= F x .8

Torque created by 4 rockets = 4 x .8 F = 3.2 F

3.2 F = I x α

3.2 F =  2.72 x   .48333

F = 0 .41 N