How Does Angular Acceleration Affect Spacecraft and Clock Movements?

[syncstarr]

[COLOR="red
1.QUESTION: [COLOR="Black"]The moon orbits Earth in 27.3 days. suppose a spacecraft leaves the moon and follows the same orbit as the moon. if the spacecraft has a constant angular acceleration of 1.0 X 10^ -10 rad/s 62 what is its angular speed after 12h of flight? (Hint: At take off the spaceship has the same angular speed as the moon)

MY ANSWER:
given: angular acceleration =1.0X 10^-10 rad/s^2
t=12hours w final=?

equation: w final = w initial + angular accelerationt
=0+1.0X 10^-10(12)
=1.2 X 10^-9 rad/sec^2[/COLOR][/COLOR]
Is this correct?? is my work and answer correct??

2. Consider a common analog clock. at midnight the hour and minute hands coincide. then the minute haand begins to rotate away from the hour hand. suppose you adjust the clock by pushing the hour hand clockwise with a constant acceleration. after 60.0 min, the hour hand has the same angular speed as the minute hand. calculate the hour hands angular acceleration.

my answer/work:
givn:
angular acceleration=?
w initial =12
w finial=60.0
t=1
equation:
w final= w initiaila+(angular acceleration )(t)
60=12+ angular acceleration (1)
60-12= angular acceleration
48 rad/s

are these the correct work and answers to these two problems? if you know either or both please let me know by leaving me a comment! THANK YOU VERY MUCH FOR TAKING THE TIME TO READ THIS! i just want to check parts of my homework problems that i am unsure about. so if you can help me please do. THANKs

 

[radou]

First of all, I assume your post would have been answered earlier if you used the homework template. Anyway,

[COLOR="red
1.QUESTION: [COLOR="Black"]The moon orbits Earth in 27.3 days. suppose a spacecraft leaves the moon and follows the same orbit as the moon. if the spacecraft has a constant angular acceleration of 1.0 X 10^ -10 rad/s 62 what is its angular speed after 12h of flight? (Hint: At take off the spaceship has the same angular speed as the moon)

MY ANSWER:
given: angular acceleration =1.0X 10^-10 rad/s^2
t=12hours w final=?

equation: w final = w initial + angular accelerationt
=0+1.0X 10^-10(12)
=1.2 X 10^-9 rad/sec^2[/COLOR][/COLOR]
Is this correct?? is my work and answer correct??

I can't figure out what you've done here. You didn't find the initial angular velocity, did you? Further on, convert days to seconds, and then calculate.

2. Consider a common analog clock. at midnight the hour and minute hands coincide. then the minute haand begins to rotate away from the hour hand. suppose you adjust the clock by pushing the hour hand clockwise with a constant acceleration. after 60.0 min, the hour hand has the same angular speed as the minute hand. calculate the hour hands angular acceleration.

my answer/work:
givn:
angular acceleration=?
w initial =12
w finial=60.0
t=1
equation:
w final= w initiaila+(angular acceleration )(t)
60=12+ angular acceleration (1)
60-12= angular acceleration
48 rad/s

are these the correct work and answers to these two problems? if you know either or both please let me know by leaving me a comment! THANK YOU VERY MUCH FOR TAKING THE TIME TO READ THIS! i just want to check parts of my homework problems that i am unsure about. so if you can help me please do. THANKs

It seems to me you are mixing up angular velocities with time.

 

[m2003]

Yes, your work and answers for both problems are correct! For the first problem, you correctly used the equation w final = w initial + angular acceleration * t to calculate the final angular speed of the spacecraft after 12 hours. And for the second problem, you used the same equation w final = w initial + angular acceleration * t to calculate the angular acceleration of the hour hand. Great job! Keep up the good work in your studies of angular kinematics.