Angular impulse and angular momentum questions

In summary: Anyways, thanks again for the help!In summary, the conversation discusses two questions and their solutions related to angular impulse and angular momentum. The first solution involves a negative value for the impulse due to its direction being opposite to the direction of rotation. The second solution has a slight difference from the textbook answer, but it is deemed accurate.
  • #1
max1205
14
0
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.
 
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  • #2
Maybe the given answers is incorrect.
 
  • #3
The correct answers according to the teextbook are:

1) 5.6 mg-m^2/s

2) 0.0817 kg-m^2/s
 
  • #4
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. :biggrin:

-Hoot:smile:
 
  • #5
Hootenanny said:
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. :biggrin:

-Hoot:smile:


But still how did they get "mg" for answer #1? how did they convert this?
 
  • #6
max1205 said:
But still how did they get "mg" for answer #1? how did they convert this?

Ahh I see your point, missed that :blushing: . 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
 
  • #7
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.
 
  • #8
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.
 

What is angular impulse?

Angular impulse is the change in the angular momentum of an object. It is defined as the product of the torque applied to an object and the time interval over which it is applied.

How is angular impulse related to angular momentum?

Angular impulse is directly related to angular momentum, as it is the cause of changes in an object's angular momentum. Specifically, the angular impulse acting on an object is equal to the change in its angular momentum.

How is angular impulse calculated?

Angular impulse is calculated by multiplying the torque applied to an object by the time interval over which it is applied. Mathematically, it can be represented as J = τΔt, where J is angular impulse, τ is torque, and Δt is time.

What is the principle of conservation of angular momentum?

The principle of conservation of angular momentum states that the total angular momentum of a closed system remains constant, unless acted upon by an external torque. This means that the angular momentum of a system will remain constant even if the system experiences internal forces, as long as no external torque is applied.

How is the principle of conservation of angular momentum applied in real-life situations?

The principle of conservation of angular momentum is applied in various real-life situations, such as in sports, where athletes use their body's angular momentum to perform movements such as spins and flips. It is also used in space exploration, where spacecrafts use the conservation of angular momentum to maintain their orientation and stability in zero-gravity environments.

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