- #1

MichaelTam

- 93

- 6

- Homework Statement
- The question is comes from MIT.

- Relevant Equations
- The equation are π(π+Ξπ)βπ(π)=Ξπππ, find T(r).

The whole question is:

One end of a uniform rope of mass π1 and length π is attached to a shaft that is rotating at constant angular velocity of magnitude π. The other end is attached to a point-like object of mass π2. Find π(π), the tension in the rope as a function of π, the distance from the shaft.

Assume that the radius of the shaft is much smaller than π. You may also ignore the effect of gravitation - assume the shaft is rotating fast enough so that the mass and the rope are almost horizontal. Express your answer in terms of some or all of the following variables: m_1 for π1, m_2 for π2, omega for π, π and π.

I can βt find the picture only website, you can find the picture at

https://ocw.mit.edu/courses/physics/8-01sc-classical-mechanics-fall-2016/week-4-drag-forces-constraints-and-continuous-systems/problem-set-4/

My misunderstanding is the difference between l and r and the relationship in the question .

πΜ :π(π+Ξπ)βπ(π)=Ξπππ where ππ is the radial acceleration, ππ=βπ^2π . Using that Ξπ=π_1/(l)

One end of a uniform rope of mass π1 and length π is attached to a shaft that is rotating at constant angular velocity of magnitude π. The other end is attached to a point-like object of mass π2. Find π(π), the tension in the rope as a function of π, the distance from the shaft.

Assume that the radius of the shaft is much smaller than π. You may also ignore the effect of gravitation - assume the shaft is rotating fast enough so that the mass and the rope are almost horizontal. Express your answer in terms of some or all of the following variables: m_1 for π1, m_2 for π2, omega for π, π and π.

I can βt find the picture only website, you can find the picture at

https://ocw.mit.edu/courses/physics/8-01sc-classical-mechanics-fall-2016/week-4-drag-forces-constraints-and-continuous-systems/problem-set-4/

My misunderstanding is the difference between l and r and the relationship in the question .

πΜ :π(π+Ξπ)βπ(π)=Ξπππ where ππ is the radial acceleration, ππ=βπ^2π . Using that Ξπ=π_1/(l)

*Ξπ , the equation above becomes: π(π+Ξπ)βπ(π)=βΞπ*π_1*π*π^2*π. The equation set up byΞπ=π_1/(l)*Ξπ is from the tension*formula. However this is the point where I donβt understand.I had separate T(r) into T_1 and T_2 , but I donβt know what is the next step?