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John100861

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- Homework Statement
- (a) A disk of mass M and radius R is held up by a massless string, as

shown in Fig. 2.12. The surface of the disk is frictionless. What is

the tension in the string? What is the normal force per unit length

that the string applies to the disk?

- Relevant Equations
- ΣF=0

The first part is easy, we have 2T= Mg

T= 0.5 Mg

Now for the second part where I'm having trouble understanding Morin's solution:

I take the normal force on a small circle arc to be N, we know that the y component of the normal force must be balance with Mg for the whole disk, therefore

Ny = Nsin(θ)

dNy= Ncos(θ)dθ

Ncos(θ)dθ= Mg

And this is where I have trouble, I end up with Mg= 0 when plugging in the limits [0, π]

Morin's solution suggests that the normal force in the arc should be written as Ndθ but I don't understand why. Please point out what's wrong with my approach, and help me understand the solution, thanks.

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