Angular Momentum and Acceleration in a Pulley System: Calculations and Equations

[mshmsh_2100]

Homework Statement

A block of mass m1 is attached to a block of mass m2 by an ideal rope passing over a pulley of mass M and radius R as shown. The pulley is assumed to be a uniform disc rotating freely about an axis passing through its center of mass (cm in the figure). There is no friction between block 2 and the surface. Assume that the pulley rotates counterclockwise as shown with an angular speed ω and that the rope does not slip relative to the pulley, and that the blocks move accordingly and do not topple or rotate.

Consider the system to be formed by the pulley, block 1, block 2 and the rope.

1. Calculate the magnitude of the angular momentum of the system about the center of mass of the pulley. Express your answer in terms of some or all of the variables m1, m2, M, R, ω and g.

2. Find the pulley's angular acceleration. Express your answer in terms of some or all of the variables m1, m2, M, R, ω and g.

Homework Equations

angular momentum = moment of inertia x angular velocity
moment of inertia = mass x radius squared
torque = moment of inertia x angular acceleration

The Attempt at a Solution

for the first part my answer was ((m1+m2)*v*R)+(M*omega*R^2)

for the second part ((m1*g)/(m1+m2+M))/R

i just need to know what I'm doing wrong

 

[mfb]

as shown

Shown where?

moment of inertia = mass x radius squared

This is true for point-masses only, it is not true for disks.

i just need to know what I'm doing wrong

How do you know it is wrong (it is wrong)? Do you know the solution?

 

[mshmsh_2100]

no i don't know the solution but every time i try to submit my answers i got it wrong... i only have one more try and cannot figure out what is wrong with my answers?

 

[mfb]

See the comment about point-masses and disks.
Your moment of inertia of the disk is wrong.

 

[Chestermiller]

Also, I hope you realize that, in your angular momentum equation, v = ωR.

 

[vela]

no i don't know the solution but every time i try to submit my answers i got it wrong... i only have one more try and cannot figure out what is wrong with my answers?

How are we supposed to tell unless you show your work? Just posting your wrong answers isn't very helpful.

 

[ehild]

[

Homework Equations

moment of inertia = mass x radius squared

That is wrong. The moment of inertia of a homogeneous disk is mR²/2.

ehild