How to Calculate Tension in a Rotating Disk System?

[henryli78]

Homework Statement

A 0.70-kg disk with a rotational inertia given by MR^2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip, then as the mass falls and the cylinder rotates, the suspension holding the cylinder pulls up on the cylinder with a force of:
A. 6.9 N
B. 9.8 N
C. 16 N
D. 26 N
E. 29 N
Answer: B

Homework Equations

∑$\tau$ = I$\alpha$
∑F = ma
a = $\alpha$r

The Attempt at a Solution

Honestly I'm not very sure how to begin. The two upwards acting forces seem to be the Tension forces of the string + suspension, while the downwards forces seem to be the weights of the objects. I am unsure how to relate the rotational inertia of the disk/cylinder with the tension forces, seeing that we don't know the net torque of the system (no angular acceleration).

Can someone direct me and maybe give me a hint on where to start? Much appreciated.

 

[tiny-tim]

hi henryli78!

draw two free body diagrams, one for the mass and one for the disk (cylinder)

do F = ma for the mass, and F = ma and τ = Iα for the disk …

show us what you get ​

 

[CWatters]

Hint: The 2kg object is accelerating downwards pulling on the string and spinning up the cylinder.

the downwards forces seem to be the weights of the objects.

Not if the 2kg object is accelerating downwards.

 

[henryli78]

Ok I get:
For the mass: m_1*g - T_1 = m_1*a
For the disk: mg + T_1 = T_2
I*alpha = T_1*r

Is this ok so far?

 

[haruspex]

Ok I get:
For the mass: m_1*g - T_1 = m_1*a
For the disk: mg + T_1 = T_2
I*alpha = T_1*r

Is this ok so far?

Yes. you need one more equation. Have you got it?

 

[henryli78]

Do you mean alpha = a/r?

 

[Tanya Sharma]

Do you mean alpha = a/r?

Yes...

 

[Malverin]

Homework Statement

A 0.70-kg disk with a rotational inertia given by MR^2/2 is free to rotate on a fixed horizontal axis suspended from the ceiling. A string is wrapped around the disk and a 2.0-kg mass hangs from the free end. If the string does not slip, then as the mass falls and the cylinder rotates, the suspension holding the cylinder pulls up on the cylinder with a force of:
A. 6.9 N
B. 9.8 N
C. 16 N
D. 26 N
E. 29 N
Answer: B

Homework Equations

∑$\tau$ = I$\alpha$
∑F = ma
a = $\alpha$r

The Attempt at a Solution

Honestly I'm not very sure how to begin. The two upwards acting forces seem to be the Tension forces of the string + suspension, while the downwards forces seem to be the weights of the objects. I am unsure how to relate the rotational inertia of the disk/cylinder with the tension forces, seeing that we don't know the net torque of the system (no angular acceleration).

Can someone direct me and maybe give me a hint on where to start? Much appreciated.

Here you can see how to solve this in principal.
Yo-yo has not the same rotational inertia, but you can see there what equations to use to solve this.
https://wiki.brown.edu/confluence/download/attachments/2752887/Yo-yo.pdf?version=1

 

[henryli78]

Thank you! I solved it :)