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1. Homework Statement
http://urlcut.com/katrolafbeelding.gif
What is the accelaration of a point on the circumference of the disk?
2. Homework Equations
[tex]\tau[/tex] = F.R = I.[tex]\alpha[/tex]
I = M.R²/2
a = R.[tex]\alpha[/tex]
F(z) = m.g
3. The Attempt at a Solution
The mass exerts a force F(z) = m.g on the disk. This force is what puts the disk into motion with [tex]\tau[/tex] = F(z).R = m.g.R (1)
Also, as I = M.R²/2 and a = R.[tex]\alpha[/tex] and [tex]\tau[/tex] = I.[tex]\alpha[/tex]
==> [tex]\tau[/tex] = M.R.a/2 (2)
Out of (1) & (2):
m.g.R = M.R.a/2 <=> m.g = M.a/2 <=> a = 2m.g/M
The acceleration asked for is a = 2m.g/M
But the teacher's solution says: [tex]\frac{2m.g}{2m+M}[/tex]
What have I done wrong?
http://urlcut.com/katrolafbeelding.gif
What is the accelaration of a point on the circumference of the disk?
2. Homework Equations
[tex]\tau[/tex] = F.R = I.[tex]\alpha[/tex]
I = M.R²/2
a = R.[tex]\alpha[/tex]
F(z) = m.g
3. The Attempt at a Solution
The mass exerts a force F(z) = m.g on the disk. This force is what puts the disk into motion with [tex]\tau[/tex] = F(z).R = m.g.R (1)
Also, as I = M.R²/2 and a = R.[tex]\alpha[/tex] and [tex]\tau[/tex] = I.[tex]\alpha[/tex]
==> [tex]\tau[/tex] = M.R.a/2 (2)
Out of (1) & (2):
m.g.R = M.R.a/2 <=> m.g = M.a/2 <=> a = 2m.g/M
The acceleration asked for is a = 2m.g/M
But the teacher's solution says: [tex]\frac{2m.g}{2m+M}[/tex]
What have I done wrong?
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