Rotational inertia of arm lifting a cup

Click For Summary
SUMMARY

The discussion focuses on calculating the rotational inertia of Doc Holliday's forearm and the shot glass while lifting a cup. The forearm spans 18 inches and weighs 2 pounds, while the shot glass and its contents weigh 5 ounces. Participants reference the equation τ=Iα, where torque equals rotational inertia multiplied by angular acceleration. The moment of inertia is calculated using the formula I = (1/3)mL² for the arm and I = mR² for the cup, emphasizing the importance of understanding point mass and rigid body dynamics.

PREREQUISITES
  • Understanding of rotational dynamics and torque
  • Familiarity with moment of inertia formulas, including I = md²
  • Knowledge of rigid body mechanics
  • Basic principles of physics related to mass and distance
NEXT STEPS
  • Study the derivation of moment of inertia formulas for various shapes
  • Learn about the application of torque in rotational motion
  • Explore the differences between point mass and rigid body inertia
  • Investigate real-world examples of rotational dynamics in sports or physical activities
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the principles of rotational motion and inertia in practical scenarios.

lyl926
Messages
1
Reaction score
0

Homework Statement


Doc Holliday takes his last shot of whiskey. His forearm and hand spans 18" and weighs 2lbs. The shotglass and its intoxicating contents weighs 5ozs. (there are 16 ozs in one pound). Doc remains otherwise motionless as his elbow bends, tossing back the whiskey.
Calculate the rotational inertia of the arm + drink.


Homework Equations


τ=Iα (torque=rotational inertia x alpha)

and the equations in the file i attached

The Attempt at a Solution



Since the cup is point mass and that arm I think is rigid mass(?),
I used
I = (1/3)mL² + something
I don't know which of the equations from the file the something should be..
My friend used I=mR² but I'm not sure how that works..
 

Attachments

  • IMG_0001.jpg
    IMG_0001.jpg
    25.9 KB · Views: 510
Physics news on Phys.org
By definition, the moment of inertia of a point mass is md^2. Every other moment of inertia you've encountered--1/3ML^2, 2/5MR^2, 2/3MR^3, whatever--is derived from I=md^2.
 

Similar threads

Rotational Motion Question, lever arm with two masses
  • · Replies 2 ·
Replies
2
Views
2K
Rotation of Rigid Bodies: Rotating stick with disc on top
  • · Replies 9 ·
Replies
9
Views
3K
Torque, rotational inertia and angular acceleartion
  • · Replies 4 ·
Replies
4
Views
3K
Angular acceleration of a falling arm
  • · Replies 8 ·
Replies
8
Views
3K
Uniform rotating rod about a point at one end of the rod
  • · Replies 3 ·
Replies
3
Views
3K
Max ω of circular hoop rotating around a peg and oscillation
  • · Replies 1 ·
Replies
1
Views
2K
Moment of inertia of a set of spinning disks
  • · Replies 25 ·
Replies
25
Views
11K
Rotational inertia of a rod that has mass on one end
  • · Replies 1 ·
Replies
1
Views
1K
Rotational Inertia about Rotation Axis Through COM
  • · Replies 2 ·
Replies
2
Views
3K
Choosing Axis of Rotation in Cylinder Oscillation Problem
  • · Replies 1 ·
Replies
1
Views
2K