angular impulse and angular momentum questions

max1205

Hi everyone,

I am stuck on two fairly easy questions that I hope someone will be able to help me with.

Questions:

1) How much angular impulse must be supplied by the hamstrings to bring a leg swinging at 8 rad/s to a stop, given that the leg's moment of inertia is 0.7 kg-m^2 ?

my solution:

angular impulse = change in angular momentum

Tt = Iw2 - Iw1 (the numbers 2 & 1 are supposed to be subscripts standing for final and initial; I=moment of inertia; w=angular velocity)

Tt = 0 - (.7)(8)
= -5.6 kg-m^2/s

what did I do wrong?

2) A 7.27kg shot makes seven complete revolutions during its 2.5 second flight. If its radius of gyration is 2.54 cm, what is its angular momentum?

my solution:

H = mk^2w (m=mass; k=radius of gyration; w=angular velocity; H = angular momentum)

7 revolutions = (360degrees x 7)/57.3
= 43.979 rad

H = (7.27)(.0254^2)(43.979/2.5sec)
= .0825 kg-m^2/s

what did I do wrong?

thanks.

andrevdh

Maybe the given answers is incorrect.

max1205

The correct answers according to the teextbook are:

1) 5.6 mg-m^2/s

2) 0.0817 kg-m^2/s

Hootenanny

For question one it seems your textbook has defined the retarting torque force as negative.

As for question two, it just seems like a rounding error, the answers are very close to each other. If I was marking your work, I would mark both your answers correct. However, I'm not marking your work.

-Hoot

max1205

But still how did they get "mg" for answer #1? how did they convert this?

Hootenanny

Ahh I see your point, missed that . Perhaps they have a typo? The 'm' is close the the 'k' on a keyboard. My calculations agree with you, but you might want to wait to see if anyone else comes up with something before you hand your work in.

-Hoot

andrevdh

The negative in your first answer arises because the impulse need to work in the opposite direction of the direction of rotation of the leg, that is it need to stop the leg from rotating. It the impulse were positive then it would have meant that the angular momentum would increase, that is the leg would rotate faster.

If I were you I would not be worried about the slight difference between your answer and that of the textbook, it probably is a result of some approximate conversion between degrees and radians. Your conversion is the more accurate one.

max1205

Thanks for your help guys. My professor told me today that my answers were right and the textbook was wrong. I wish she could have let us know earlier.