# Inclined plane with block and cylinder, pulley with mas

## Homework Statement

Find the acceleration of the system if the mass m1 is a disk with radius R rolling down an incline which makes an angle theta with the horizontal, and the disk is connected to a pulley with mass M and radius R, which is connected to a block m2 hanging from that pulley. The system will be rotating with the disk, down the incline.

## Homework Equations

Net Torque of pulley = R(T2-T1) = Iw

Net torque of m1 = R(m1gsintheta)

Net force in x = m1gsintheta - T1 = m1a

Net force in y = m1gcostheta

## The Attempt at a Solution

I've solved this exact problem for a block sliding instead of a disk using three equations: net torque on pulley = R(T1-T2), T1 = m1(gsintheta - a), and T2 = m2(a + g). So I just used substitution and isolated a.

But I don't know how a disk as opposed to a block would change this situation, help would be appreciated, I don't have any pictures unfortunately, but its a standard inclined plane problem with a real pulley and rolling disk.

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Simon Bridge
Homework Helper
Start by isolating each mass and drawing a free-body diagram for each.
Recall how you used to handle the situation for a cylinder rolling down an incline by itself and how that is different from the case where a block is sliding down the incline.

I'm a tad bothered by the wording - you have to find the acceleration of the system, and the system is rotating with the disk... it is unclear, therefore, what "the system" means. I'm afraid we'll need a diagram to help you in any way specifically.

ehild
Homework Helper
This is the picture. Draw the free-body diagram for all objects, disk, pulley and block. Take care, the torque is equal to the moment of inertia multiplied by the angular acceleration. The disk rolls without slipping, that means a relation between its translational motion and rotation.

This is the picture.

View attachment 82223

Draw the free-body diagram for all objects, disk, pulley and block. Take care, the torque is equal to the moment of inertia multiplied by the angular acceleration. The disk rolls without slipping, that means a relation between its translational motion and rotation.
So the torque on the rolling disk will be (R)(T1) = Ia right ? Im having trouble relating this to the other given information

ehild
Homework Helper
So the torque on the rolling disk will be (R)(T1) = Ia right ? Im having trouble relating this to the other given information
You mean torque=Iα? a is the linear acceleration.

As for "rolling without slipping" you might see http://faculty.wwu.edu/vawter/PhysicsNet/Topics/RotationalKinematics/RollingWithoutSlipping.html [Broken]

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