A spinning top - moment of inertia/ Torque/ Angular momentum

[Theknight330]

Hey guys,

I have this really annoying last question on my assignment which is a pain. It combines 3 physics principles together.


I am having problems specifically with 2) 3) and 4)

2)I know that T = | r x F |, but what kind of general vector do I use to represent F?
4) I have no clue how to do this one unfortunately.

The question should be in the attached thumbnail

 

[ACPower]

The only force acting on the top is gravity.

 

[hikaru1221]

For part b, note that torque is a vector: $$\vec{T}=\vec{r}\times m\vec{g}$$ as the torque is calculated about the origin. You can express $$\vec{r}=d\hat{r}$$.

For part c, the problem has already given you the answer. Just plug moment of inertial in.

For part d, again, the problem has already shown you the way. Substitute L and T found earlier in the equation: $$\vec{T}=d\vec{L}/dt$$. You have known that the top will rotate around the Y axis beside spinning very fast about its own axis of symmetry (because of this "very fast" spin, we can achieve L as in part c). That means the $$\hat{r}$$ vector will rotate around the Y axis just like the shaft. If so, then how would you relate $$d\hat{r}/dt$$ , the angular speed of the rotation about the Y axis $$\Omega$$ and the vector $$\hat{r} \times \hat{g}$$. Note that $$\hat{g}$$ is only a unit vector whose direction is downward, nothing special. Find $$\Omega$$ and then the time needed.

 

[lol_john]

Nice one Jong trying to get the internet to solve the final question.

 

[ste@mPunK]

hahahahhaa oh that's classic mate!

 

[lol_john]

hey clive this doesn't help at all so stop trying to get the answer from it.