Angular Velocity w/2 welded disks

Click For Summary
SUMMARY

The discussion centers on calculating the angular velocities of two concentric disks, one smaller (1.66 kg, radius 12.4 cm) and one larger (6.85 kg, radius 24.8 cm), when two identical masses (800 g each) are released from rest. The problem requires applying principles of rotational dynamics and energy conservation to determine the angular velocity of both disks and the linear velocity of the masses when they are 60.0 cm apart. The inertia formulas for both disks are given as I = 1/2 m R², which are crucial for solving the problem.

PREREQUISITES
  • Understanding of rotational dynamics and angular velocity
  • Familiarity with the moment of inertia calculations
  • Knowledge of Newton's second law applied to rotational systems
  • Basic principles of energy conservation in mechanical systems
NEXT STEPS
  • Study the application of Newton's second law to rotational motion
  • Learn about the conservation of energy in mechanical systems
  • Explore the concept of moment of inertia for various shapes
  • Practice problems involving angular velocity and linear velocity relationships
USEFUL FOR

Students studying physics, particularly those focusing on rotational dynamics, as well as educators seeking to enhance their teaching of angular motion concepts.

CollegeStudent
Messages
109
Reaction score
0

Homework Statement



Two concentric disks attached to each other form a single unit. This two disk unit is mounted onto a frictionless horizontal axle through the center hole. Two strings are attached and wound in opposite directions around the outer perimeter of each disk and are left hanging. The smaller disk has a mass of 1.66 kg and a radius R1 of 12.4 cm. The larger disk has a mass of 6.85 kg and a radius R2 of 24.8 cm. (a) If two identical masses of 800 g are hung from both strings and the two masses are released from rest from the same initial height what will be the angular velocity of the larger disk when the two masses are 60.0 cm apart? What will be the angular velocity of the smaller disk and the linear velocity of each mass at the same instant? (Figure 3)


Homework Equations





The Attempt at a Solution



well I'll write down all the variables given

*smaller* *larger* *mass1* *mass2*
r1 = 12.4cm r2 = 24.8cm m1 = 800g m2 = 800g
m1 = 1.66kg m2 = 6.85kg


what we want is ω of larger disk, ω of smaller disk, and V_f of each mass

Im not really sure where to get started here.

Inertia of smaller disk = 1/2mR²
Inertia of larger disk = 1/2mR²


any hints here?
 
Physics news on Phys.org
You can either use dynamics (applying Newton's 2nd law to all three objects) or energy conservation.
 

Similar threads

Perfectly inelastic collision of two moving and rotating disks
  • · Replies 9 ·
Replies
9
Views
3K
Calculating angular frequency and velocity after a collision
  • · Replies 10 ·
Replies
10
Views
2K
Conservation of Energy and Angular Momentum in a Rotating Train-Disk System
  • · Replies 30 ·
2
Replies
30
Views
4K
Calculating Angular Velocity of Disk w/ Angular Momentum
  • · Replies 1 ·
Replies
1
Views
1K
Inertia and Angular Acceleration
  • · Replies 3 ·
Replies
3
Views
2K
A doubt in angular momentum problem
  • · Replies 4 ·
Replies
4
Views
1K
Angular velocity of a solid disk
  • · Replies 17 ·
Replies
17
Views
8K
What is the final angular velocity when two rotating disks are pushed together?
  • · Replies 5 ·
Replies
5
Views
7K
Angular speed calculation after an inelastic collision
  • · Replies 20 ·
Replies
20
Views
3K
Two Rotating Disks Contacting Along Edge
  • · Replies 2 ·
Replies
2
Views
2K