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(II) To get a flat, uniform cylindrical satellite spinning at the correct rate, engineers fire four tangential rockets as shown in Fig. $56 .$ If the satellite has a mass of $3600 \mathrm{kg},$ a radius of $4.0 \mathrm{m},$ and the rockets each add a mass of $250 \mathrm{kg},$ what is the required steady force of each rocket if the satellite is to reach 32 rpm in 5.0 min, starting from rest?

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31$N$

Physics 101 Mechanics

Chapter 10

Rotational Motion

Rotation of Rigid Bodies

Dynamics of Rotational Motion

Equilibrium and Elasticity

Rutgers, The State University of New Jersey

University of Washington

Hope College

Lectures

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

03:25

(II) To get a flat, unifor…

0:00

02:29

04:42

To get a flat, uniform cyl…

04:04

01:17

07:20

A space station is constru…

10:00

A 250 -lb satellite has a …

07:32

The 200 -kg satellite has …

So here we know that the firing force of the rockets will create a net torque, but no net force. Um, since each rocket fires tangentially, each force has a lever arm equal to the radius of the satellite and each forces perpendicular to that lever arm. So we can say that the net torque would be equal to four times are given that we have four rockets. Ah, and then we can say that this is gonna be equal to ay the moment of inertia times the angular acceleration where the moment of inertia would be equal to 1/2 m r squared, which would be the moment of inertia of the cylinder, plus four times lower case R lower case M R squared. This would be the four point we would be treating the rockets. That's four point masses. Ah, the angular acceleration. Ah would, of course, be equal to Delta Fada over Delta Omega over Delta T therefore weekend, then combined these two equations and simply say that four times fr ah would be equal to again. I times Alfa, or we can say 1/2 times m r squared plus four lower case m r squared multiplied by Delta Omega with respect to time and let's solve for the force. So force is then going to be equal to 1/2 Um, plus four times and times are times delta omega all over four times delta t. And at this point, we can solve. So the force of each rocket essentially ah, would be 1/2 times 3600 kilograms plus four times 250 kilograms multiplied by 4.0 meters, multiplied by 32 revolutions per minute, multiplied by two radiance for everyone. Revolution multiplied by one minute for every 60 seconds. And this will all be divided by four times five minutes multiplied by 60 seconds for every one minute. Ah, and we have that the force is gonna be equal to 30 1.3 Newton's. This is our final answer. That is the end of the solution. Thank you for watching

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