Solving Rotational Motion: 4kg Disk & 4.0kg + 8.0kg Masses

Click For Summary
SUMMARY

The discussion centers on calculating the angular velocity of a 4kg disk with a 0.20m radius, subjected to a 4.0kg and an 8.0kg mass connected by a massless string. The participant initially calculated the angular velocity to be 28 radians/second after 2 seconds, but received guidance to use the conservation of kinetic and potential energy instead of focusing on tensions in the string. The final conclusion indicates that the participant successfully resolved the problem with the help of the forum members.

PREREQUISITES
  • Understanding of rotational dynamics and angular motion
  • Familiarity with the moment of inertia formula, I = 1/2mr^2
  • Knowledge of the relationship between linear and angular velocity
  • Basic principles of conservation of energy in mechanical systems
NEXT STEPS
  • Study the conservation of mechanical energy in rotational systems
  • Learn how to calculate torque and its relationship to angular momentum
  • Explore advanced rotational dynamics problems involving multiple masses
  • Investigate the effects of friction and slipping in rotational motion scenarios
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators looking for examples of problem-solving in dynamics.

Mugen112
Messages
15
Reaction score
2

Homework Statement



A disk with a mass of 4kg and a .20m radius is free to rotate about a horizontal axis. A 4.0kg mass and a 8.0kg mass are attached by a massless string, which is hung over the disk. If the string does not slip, what is the angular velocity of the disk after 2 seconds?

Homework Equations



Angular acceleration = change in angular velocity/change in time
I= 1/2mr^2
Angular velocity= tangential velocity/radius

The Attempt at a Solution



I took a picture of my work. It looks like I did everything right, but I'm not sure. I thought I would use inertia in my problem solving, but I didn't need it?? All I did was, I found the acceleration of the heavier block using the formula in the picture (which includes the mass of the disk). I took that acceleration, which should equal the tangential acceleration, and found the tangential velocity after 2 seconds. With the tangential velocity, I found the angular velocity using the radius of the disk shown in the picture. Found it to be 28 rads/sec which is about 44 revolutions per second. I think this would be pretty fast when dealing with only 4 and 8kg weights... Is this correct? If you can't make something out in the picture, let me know. THANKS!

2979978092_ab59a29d50_o.jpg
 
Physics news on Phys.org
Hi Mugen112! :smile:

I don't follow what you've done … I particularly don't follow your T1 - T2 equation … you would need torque = rate of change of angular momentum.

But why bother to find T1 and T2 when the question doesn't ask for them?

Just use KE + PE = constant. :smile:
 


I figured it out! Thanks for the help!
 

Similar threads

Perfectly inelastic collision between Projectile and a hinged disk
  • · Replies 26 ·
Replies
26
Views
2K
What is the net acceleration of the coin on a rotating disk?
  • · Replies 2 ·
Replies
2
Views
2K
Solving Jumping Off a Disk Problem (d)
  • · Replies 24 ·
Replies
24
Views
3K
Conservation of Energy and Angular Momentum in a Rotating Train-Disk System
  • · Replies 30 ·
2
Replies
30
Views
4K
System of two wheels of different sizes with an axle through their centers
  • · Replies 67 ·
3
Replies
67
Views
5K
Friction and Rotation: Understanding the Ratio of Forces on a Rotating Disk
  • · Replies 5 ·
Replies
5
Views
1K
Rubber on a rotating disk (angular velocity, forces)
  • · Replies 6 ·
Replies
6
Views
2K
Determining the Speed of a Rotating Disk with a Constant Force
  • · Replies 10 ·
Replies
10
Views
3K
Graduate Mass dropped onto rotating disk
  • · Replies 5 ·
Replies
5
Views
3K
Moment of Inertia of a Rotating Disk
  • · Replies 1 ·
Replies
1
Views
2K