Rotational Motion - 2 Disc System

In summary: This makes sense because the larger disk has a bigger moment of inertia, so it requires more torque to produce the same angular acceleration.
  • #1
HoodedFreak
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0

Homework Statement


Two metal disks, one with radius R1 = 2.50 cm and
mass M1 = 0.80 kg and the other with radius R2 = 5.00 cm and
mass M2 = 1.60 kg, are welded together and mounted on a frictionless
axis through their common center, as in Problem 9.77.
(a) A light string is wrapped around the edge of the smaller disk,
and a 1.50-kg block is suspended from the free end of the string.
What is the magnitude of the downward acceleration of the block
after it is released? (b) Repeat the calculation of part (a), this time
with the string wrapped around the edge of the larger disk. In which
case is the acceleration of the block greater? Does your answer
make sense?

Homework Equations


T = I * α
a = α * R
I of a cylinder = MR^2/2
T = F * l

The Attempt at a Solution


a) The block is enacting a torque, which is equal to the force of gravity times the lever arm.
T = 1.5g * R
where R is the radius of the smaller cylinder
The moment of inertia of the system of cylinders is MR^2/2 for the smaller cylinder + (2M)*(2R)^2/2 for the bigger cylinder = 9MR^2/2

T = I*α ⇒ 1.5gR = 9MR^2/2 * α
3g = 9MR * α
3g = 9Ma
a = g/3M = 4.09 m/s^2

The answer however is a = 2.8

What did I do wrong?
 
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  • #2
HoodedFreak said:
The block is enacting a torque, which is equal to the force of gravity times the lever arm.
T = 1.5g * R
Do not assume that the tension in the string (which is what exerts the torque) is equal to the weight of the block.
 
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Likes HoodedFreak
  • #3
Doc Al said:
Do not assume that the tension in the string (which is what exerts the torque) is equal to the weight of the block.
I see, I did that and I got the right answer, thanks alot!

I did:
T - 1.5g = m*a
T*R = 9MR^2α/2

Then I solved them to get a = 2.88 which is the answer.
and repeated the same process for b) to get a = 6.13
 

Related to Rotational Motion - 2 Disc System

1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point, causing it to rotate.

2. How does rotational motion differ from linear motion?

Linear motion refers to the movement of an object in a straight line, while rotational motion involves the movement of an object around an axis or center point.

3. How is rotational motion measured?

Rotational motion is typically measured in terms of angular displacement, velocity, and acceleration. These are represented by the symbols θ, ω, and α respectively.

4. What is the conservation of angular momentum?

The conservation of angular momentum states that the total angular momentum of a system will remain constant if no external torque is applied.

5. Can rotational motion be converted into linear motion?

Yes, rotational motion can be converted into linear motion through mechanisms such as gears and pulleys. This is known as translation motion.

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