# Rotation of a drum attached to a spring

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1. Jun 24, 2017

### Datta108

1. The problem statement, all variables and given/known data
Rotation of a small drum of mass moment of inertia 0.44kg.m^2 and with frictional resistance torque 0.3 N.m is initiated by a string wound around its 20 mm diameter shaft and attached to a stretched spring, as shown in the figure. If the spring, which has a stiffness 2N/mm is initially stretched by 120 mm before the drum is released from rest, determine the maximum angular velocity, in rpm, attained by the drum.

2. Relevant equations
Tnet = Iα
SE = 1/2 kx^2
KE of drum = 1/2Iw^2

3. The attempt at a solution
The spring energy provided by the stretched spring is given to the drum and converted to the kinetic energy of the drum. Equating these two gives w = 23.4 rad/s^2. I don't know how to proceed from here. I believe we have to find the T provided by the spring. Then, the first equation can be used to find the difference in T and therefore alpha can be found. From this v can also be found. However, I am stuck at finding T provided by spring.

Any help (ASAP) will be greatly appreciated.

Many Thanks!

2. Jun 24, 2017

### haruspex

That is not going to help since the peak rate isprobably reached before the spring becomes slack.
There is no difficulty finding the initial tension, is there?
Consider when the spring has contracted by a distance x from its initial stretch. What work has been done by the spring? What is the KE of the drum?

3. Jun 24, 2017

### scottdave

Using the frictional torque and the radius, you can find an effective "frictional force" acting at the edge.

4. Jun 24, 2017

### Datta108

Sorry, did you mean torque?

Work done by the spring would be 1/2kx^2.
Won't the KE of the drum equal the SE of the spring?

Sorry if I am asking stupid questions here, but my tutor did not go over such problems in detail.
(This is NOT to complete my homework by the way. I am studying for an exam that's coming up)

5. Jun 24, 2017

### Datta108

Do you mean 0.3 N.m * 0.010 m?

6. Jun 24, 2017

### scottdave

Look at the units. You want to divide (0.3 N*m) / (0.01 m) to get 30 Newtons of friction, which works against motion of the drum (so it is in opposite direction of spring force).

7. Jun 24, 2017

### haruspex

No. It started with extension L (=0.12m) and I defined x as the reduction in extension, so:
- what PE did the spring start with? (Use L, not the numerical value.)
- what PE does it still have?
- what work has it done?
No, there s friction. How much work has been done against that?

8. Jun 25, 2017

### Datta108

Sorry, I am not able to think about this problem. Could you please give me a step by step method for this question?
I have a mechanics exam tomorrow. Thank you.

9. Jun 25, 2017

### Staff: Mentor

Sorry, helpers are not permitted to provide step by step solutions for homework problems. They can offer hints and point out errors in work you've shown, or offer suggestions concepts to think about or try.

10. Jun 25, 2017

### Datta108

Sorry, I was not aware of this. Thank you all!