Speed of a ball rolling down an incline

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SUMMARY

The discussion focuses on calculating the speed of a hollow basketball rolling down a 30° incline after traveling 8.4 m. The key approach involves using the conservation of energy principle, which accounts for both translational and rotational kinetic energy. The relationship between linear speed (v) and angular speed (ω) is defined by the equation v = ωR, where R is the radius of the basketball. The mass of the basketball is not required for the calculations as it cancels out in the energy equations.

PREREQUISITES
  • Understanding of conservation of energy principles
  • Familiarity with rotational dynamics and kinetic energy
  • Knowledge of the relationship between linear and angular motion
  • Basic algebra for manipulating equations
NEXT STEPS
  • Study the conservation of energy in rolling motion
  • Learn about the moment of inertia for hollow spheres
  • Explore the relationship between linear velocity and angular velocity in detail
  • Practice similar problems involving rolling objects on inclines
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Students studying physics, particularly those focusing on mechanics and dynamics, as well as educators looking for examples of energy conservation in rolling motion.

captainjack
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Homework Statement



A hollow basketball rolls down a 30\circ incline. If it starts from rest, what is its speed after it's gone 8.4 m along the incline?

Homework Equations



v=\omegaR

The Attempt at a Solution



I don't really know where to start with this. I've done similar problems, but I was given the mass of the rolling object. What equations would I need to manipulate so that I don't need the mass or radius of the basketball? I feel like this is a fairly simple problem, but my professor never showed us how to do one without mass, and the book doesn't explain either.

I know that to receive help here I'm supposed to have made an attempt at the problem, but I would greatly appreciate any help. Even if it is just a few equations that I should be looking at.
 
Last edited:
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hi captainjack! :smile:

(have an omega: ω :wink:)

call the mass "m" and the radius "r", and use conservation of energy, with your rolling constraint v = ωr …

what do you get? :smile:​
 
Just call the mass m, and the radius of the ball be R. They will cancel.
Conservation of energy is very useful for such problems. The ball rolls, so it has both translational and rotational kinetic energy, and rolling means that the speed of translation and the angular speed of rotation are related as v=wR.

Edit:Tiny-tim beat me ...

ehild
 
Thank you so much (: figured it was some super important rule I was forgetting XP
 

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