Question

In the limit that the moment of inertia I→0 while the mass m remains finite, what magnitudes would you expect for the tension T in the vertical section of string and the downward acceleration a of the center of mass?

Answer 1

Here are the possible answers:
T=0 and a=0
T=0 and a=g
T=mg and a=0
T=∞ and a=g
T=0 and a=∞
T=mg and a=g

Answer 2

can you please post the diagram

Answer 3

thank you...lets have a look....

Answer 4

so if I approaches zero but mass is finite, what must be changing in the disc?

Answer 5

its 0

Answer 6

no...what physical property of the disc must be changing for I to approach zero but the mass is finite.

Answer 7

i dont understand

Answer 8

ok...lets assume the object shown is a disc...what is the formula for the moment of inertia of a uniform disc?

Answer 9

I=.5mr^2

Answer 10

great so if I approaches zero but the mass is finite , what happens to the radius?

Answer 11

it stays the same?

Answer 12

If I is approaching zero then the radius must also be getting smaller because mass is constant

Answer 13

ok

Answer 14

so the disc gets smaller and smaller until it looks like a point mass...agreed?

Answer 15

yes

Answer 16

Draw a FBD with a point mass on the end and a string attached to it.
What is the tension in the string?

Answer 17

oops typo...
Draw a FBD of the point mass, what is the tension in the spring?

Answer 18

lmao...string

Answer 19

is the tension 0

Answer 20

no the weight is on the end...

Answer 21

is it mg

Answer 22

good, now what is the acceleration of the center of mass?

Answer 23

g

Answer 24

not quite

Answer 25

0

Answer 26

good

Answer 27

so the answer is T=mg and a=0

Answer 28

@surry99

Answer 29

yes

Answer 30

it was wrong

Answer 31

@surry99

Answer 32

what was wrong?

Answer 33

the answer

Answer 34

T = mg a = g

Answer 35

It is very late where I am goodnight

Answer 36

is still wrong