What is the angular momentum of uncle's tire immediately upon its departure?

Click For Summary
SUMMARY

The angular momentum of the tire upon its departure is calculated using the formula L = I * ω, where I is the moment of inertia and ω is the angular velocity. For a solid cylinder, the moment of inertia I is given by (1/2) * m * r². Given a tire mass of 10 kg and a radius of 0.3 m, the angular momentum is determined to be 4.2 kg m²/s when the tire is moving at a velocity of 2.8 m/s. The discussion also touches on the subsequent motion of the tire as it travels up an embankment at a 30° angle.

PREREQUISITES
  • Understanding of angular momentum and its calculation
  • Familiarity with the moment of inertia for solid cylinders
  • Basic knowledge of kinematics and energy conservation
  • Ability to perform trigonometric calculations involving angles
NEXT STEPS
  • Study the derivation of angular momentum formulas for different shapes
  • Learn about the conservation of energy in mechanical systems
  • Explore the effects of incline on the motion of objects
  • Investigate the relationship between linear and angular velocity
USEFUL FOR

Physics students, mechanical engineers, and anyone interested in understanding the principles of angular momentum and motion dynamics.

mattmannmf
Messages
170
Reaction score
0
As you approached the I-74 exit in your uncle's little red sports car convertible you happened to notice a cat crossing the road. Not that you have any particularlove of cats (especially this one whose snooty disposition seems to beckon for a game of chicken) you swerve out of the way spilling scalding hot coffee all over your new summer duds.

Unknown to you at the time, the auto mechanic, having had an uneventful social life and being consequently somewhat incoherent, had inadvertently forgotten to fasten the lug nuts on one of your uncle's tires.

Given your velocity on the exit ramp as 2.8 m/s, a tire mass of 10 kg and radius 30 cm;

(a) What is the angular momentum of uncle's tire immediately upon its departure? (Assume the tire is a solid cylinder) in kg m2/s?


(b) Next, the tire cruises up an embankment at 30° for 1 meter beforelaunching across Piranha Lake. What is the velocity of the tire at the topof the embankment in m/s?

not sure where to start for this one
 
Physics news on Phys.org
i figured out that angular momentum is 4.2
 
Inital KE of the tire is 1/2*M*V2 + 1/2*I*(V/R)2; both rotational and translational
Final KE = Initial KE - M*g*h where h = 1m * sin(30°).

i just plugged in the numbers and got 2.42...wrong.
 
Hi mattmannmf! :smile:
mattmannmf said:
i figured out that angular momentum is 4.2

Nooo … how did you get that? :confused:
 
its rmvsin (30), i just plugged in the numbers and got 4.2...im sure its correct because it told me it was correct
 
mattmannmf said:
its rmvsin (30) …

No, the 30º is in part (b) …

this is for part (a), where the road is level …

you have the speed of the tyre, so what is the angular momentum?
 

Similar threads

Rotational Speed: Calculating Final Velocity on Embankment
  • · Replies 2 ·
Replies
2
Views
5K
What is the Angular Momentum of a Spinning Disk Subject to Applied Forces?
  • · Replies 10 ·
Replies
10
Views
4K
Can You Solve These College Physics Problems on Energy and Momentum?
  • · Replies 14 ·
Replies
14
Views
11K