Solved: Rotational Dynamics | Angular Speed=3.1 rad/sec

Click For Summary
SUMMARY

The discussion focuses on calculating the angular speed of a thin uniform rod pivoting about a frictionless pin. The rod, with a length of 2.0 m, is released from an angle of 40 degrees above the horizontal. Using the principle of conservation of energy, the angular speed is determined to be 3.1 rad/sec. The solution involves applying the equation for linear velocity (v = 6.26 m/s) and converting it to angular speed using the formula ω = v/r.

PREREQUISITES
  • Understanding of rotational dynamics and angular motion
  • Familiarity with the principle of conservation of energy
  • Knowledge of moment of inertia calculations, specifically I = (1/12)ML²
  • Ability to apply kinematic equations for rotational motion
NEXT STEPS
  • Study the derivation and application of the conservation of energy in rotational systems
  • Learn about calculating rotational kinetic energy using KE = 0.5Iω²
  • Explore the relationship between linear and angular velocity in different pivot scenarios
  • Investigate the effects of friction and other forces on rotational motion
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational dynamics, as well as educators looking for practical examples of energy conservation in rotational systems.

iamkristing
Messages
33
Reaction score
0
[SOLVED] rotational dynamics

Homework Statement


A thin uniform rod has length 2.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest as angle theta=40 above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position.


Homework Equations





The Attempt at a Solution



I used mgh=.5mv^2 and found v=6.26

Since w=v/r I found the angular speed to be 6.26/2=3.1 rad/sec

I think this is how the problem is worked out...I'm just not sure. Thanks!
 
Physics news on Phys.org
What about the rotational KE?
 
Would the rotational KE be .5Iwf^2?

Where I=(1/12)ML^2 and then you just add that on to the final kinetic energy and solve for vf?
 
You could find the total KE by adding the KE of the center of mass to the rotational KE about the center of mass. But much easier to treat the rod as purely rotating about one end.
 
ok thanks I got it!
 

Similar threads

Question about springs and rotational/translational energy
  • · Replies 4 ·
Replies
4
Views
2K
Rotating rod of negligible mass attached to two point masses
  • · Replies 19 ·
Replies
19
Views
4K
Dynamics of Rotational Motion and hinge
  • · Replies 2 ·
Replies
2
Views
3K
Rotational Momentum: Calculating Angular Speed After Cockroach Stops
  • · Replies 2 ·
Replies
2
Views
2K
Uniform rotating rod about a point at one end of the rod
  • · Replies 3 ·
Replies
3
Views
2K
Conservation of angular momentum
  • · Replies 22 ·
Replies
22
Views
4K
A uniform rod allowed to rotate about an axis and then it breaks
  • · Replies 18 ·
Replies
18
Views
3K
Calculating Angular Speed of Rotating Apparatus with Attached Mass and Rod
  • · Replies 1 ·
Replies
1
Views
2K
What is the Angular Speed of a Rod Pivoted at One End?
  • · Replies 8 ·
Replies
8
Views
4K
Rotations from angular acceleration and final angular velocity
  • · Replies 3 ·
Replies
3
Views
1K