Solved: 4 Rotation Problems Homework

[hannibalisfun]

Homework Statement

1. A 8 cm radius disk with a rotational inertia of .12 kg * M(squared) is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10 kg mass hangs from the other end. The mass is raised by using a crank to apply a 9 N * m torque to the disk. The acceleration of the mass is:

2. A small disk of radius R1 is mounted coaxially with a larger disk of radius R2. The disks are securely fastened to each other and the combination is free to rotate on a fixed axle that is perpendicular to a horizontal frictionless table top. The rotational inertia of the combination is l. a string is wrapped around the larger disk and attached to a block of mass M, on the table. Another string is wrapped around the smaller disk and is pulled with a force F, parallel to the table. The acceleration of the block is:

3. A block of mass m is tied to a light cord that is wrapped around a spoked pulley which has most of its mass Mp, around its rim and which has a radius R. The other end of the cord is attached to a block of mass M resting on a rough horizontal surface. There is no friction in the pulley. Find an expression for the acceleration of the block and the tension in the cord in terms of m, M, Mp, R, ad g as needed.

4. i know that the constant angular acceleration, 5, the intial angular volocity, 45, the angular distance it travel, 360 rad, and the time it took to travel that, 6 secs. i need to find the work it does.

Homework Equations

The Attempt at a Solution

1. the way i tried to solve it was i set up this equation and tried to solve for T. (9, torque from the crank, - T * .08, radius in meters,) = .12, rotiational intertia, * A, acceleration of the mass,/.08, radius in meters. then i subsituted the T value i got for T into T - m * g= m * A

2. i not sure how to do this one but we did this one in class and i think the answer might be ( R1 * R2 * F)/(1 + (M * R1 * R2))

3. I know I = Mp * R * R. I could work this problem if there was not a second mass because i would just solve for -T * R = Mp * R * A. But with the second mass I'm not sure how you take that into account.

4. i have no clue how to work this one because all the equation i have need rotational intertia to find the work.

 

[OlderDan]

Posting multiple problems in one thread often leads to confusion as people respond to different parts of the set. Please post your problems separately unless the solutions to one problem is used in another.

Paraphrasing, as you have done in number 4 usually obscures the problem you are trying to solve. I have only a cloudy idea what the "it" is in "i need to find the work it does". Please state the problem exactly the way it was given to you.

 

[m2003]

I would first like to commend you on your efforts to solve these rotational problems. It is important to use the correct equations and units when solving such problems to ensure accurate results. After reviewing your attempt at a solution, I would like to offer some suggestions and corrections.

1. Your setup for the first problem is correct, but there is a small error in your calculation. The equation should be (9 N*m - T * 0.08 m) = 0.12 kg*m^2 * A / 0.08 m. This would give you a value for T of 6.9 N*m. However, when substituting this value into the second equation, you should use the mass in kg (10 kg) instead of the weight in N (98 N). This would give you an acceleration of 0.69 m/s^2.

2. For the second problem, the correct equation to use is (R1 * R2 * F) / (R1^2 + R2^2 + l). This takes into account the moment of inertia of the two disks and the block. The value for l can be found by using the parallel axis theorem, l = M * (R1^2 + R2^2). This would give you an acceleration of F / (M + (M * R1^2 / R2^2)).

3. For the third problem, you are correct in using the equation I = Mp * R^2. However, to take into account the second mass, you need to use the equation (M + m) * A = T * R - (M + m) * g. This is because the tension in the cord is equal to the difference in forces on either side of the pulley. You can then substitute in the value for I and solve for A and T.

4. The fourth problem is asking for the work done by the object, which can be found by using the equation W = (1/2) * I * ω^2. You are given the angular acceleration, initial angular velocity, and angular distance traveled, so you can solve for the final angular velocity using the equation ω^2 = ω0^2 + 2αθ. Then, plug in the values into the work equation to find the work done.

Overall, it is important to carefully review the equations and units being used in each problem and to