# Mass and pulley system (Rotational Dynamics)

1. Dec 8, 2016

### ikihi

1. The problem statement, all variables and given/known data
Consider a pulley with a mass-less cord attached to its edge. The rope hangs a distance of d= 2.50 m below the bottom of the pulley. Attached to the end of this cord is a block with mass 3.00 kg. There is also an electric motor attached to the pulley which supplies a torque of 28.7 N * m. The pulley can be considered a disk with a radius of 0.65 m.

a) What is the torque due to the hanging block?
b) what is the moment of inertia of the pulley?
c) Once the motor is turned on the pulley begins to rotate counter clock-wise. What is the magnitude of the angular acceleration of the pulley?

2. Relevant equations
I = 0.5 * m * r^2 (moment of inertia)

3. The attempt at a solution

a) Torque= m*g*d ---> Torque = 3.00 * 9.80 * 2.50 = 73.5 N * m

b) I'm stuck on how to find the moment of inertia here because no mass was given for the pulley itself.

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2. Dec 8, 2016

### Staff: Mentor

Looks to me like there's some information missing. Is this the problem, word for word? Is it from a textbook?

3. Dec 8, 2016

### ikihi

yes that is the problem

4. Dec 8, 2016

### Staff: Mentor

More info is needed to solve the problem, even for part a. The torque on the pulley due to the hanging block depends on the tension in the cord, which cannot be solved for without additional information.

5. Dec 9, 2016

### ikihi

Okay i asked, the info was missing. The mass of the pulley is 1.3 kg.

6. Dec 9, 2016

### ikihi

Okay so the moment of inertia is 0.4225 kg * m.
The angular acceleration, that I calculated, is 1.10 m/s^2

Last edited: Dec 9, 2016
7. Dec 9, 2016

### Staff: Mentor

I think you forgot to square the radius when you calculated the moment of inertia -- check your units.

When you redo your calculation of the angular acceleration, show how you did it. (Check your units there also.)

8. Dec 9, 2016

### haruspex

That has the wrong units for angular acceleration.

9. Dec 9, 2016

### ikihi

https://pbs.twimg.com/media/CzRa737UkAAqYIj.jpg:large [Broken]

Last edited by a moderator: May 8, 2017
10. Dec 9, 2016

### haruspex

That looks lke the right answer.
But in future, please do not post working as an image. Take the trouble to type it in. That guarantees legibility and makes it possible to comment on individual lines, e.g. to point out an error. Images are really for book extracts and diagrams.

Last edited by a moderator: May 8, 2017