Finding Velocity and Angular Speed of a Rolling Cylinder

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SUMMARY

The discussion focuses on calculating the velocity and angular speed of a solid cylinder with a radius of 20 cm rolling down a 2.5 m incline without energy loss due to friction. Participants clarify that the mass of the cylinder is not required for the calculations, as it cancels out in the energy equations. The relevant equations include the moment of inertia, I = mr², and the total kinetic energy, KE = (1/2)·I·ω² + (1/2)·m·v². The final results can be derived using gravitational potential energy, E = mgh, to find both the linear and angular velocities at the bottom of the incline.

PREREQUISITES
  • Understanding of rotational dynamics and moment of inertia
  • Familiarity with gravitational potential energy equations
  • Knowledge of kinetic energy equations for both translational and rotational motion
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the derivation of the moment of inertia for various shapes, focusing on I = mr² for cylinders
  • Learn about energy conservation principles in mechanical systems
  • Explore the relationship between linear and angular velocity in rolling motion
  • Investigate the effects of friction on rolling objects and energy loss
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators looking for examples of energy conservation in rolling objects.

gamer1319
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Homework Statement



A solid cylinder of radius 20cm is released from a 2.5 high incline. If it rolls down without losing any energy to friction, find the cylinder's velocity at the bottom of the incline and the angular speed at the bottom of the incline.

Homework Equations





The Attempt at a Solution



I need to be given a mass to solve this! If I had a mass, I'd plug it into I = mr^2, find the inertia. With that, I'd plug it into E = mgh, and after i'd find W (angular velocity). Help!
 
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Are you sure the masses don't cancel out? :)
 


gamer1319 said:

Homework Statement



A solid cylinder of radius 20cm is released from a 2.5 high incline. If it rolls down without losing any energy to friction, find the cylinder's velocity at the bottom of the incline and the angular speed at the bottom of the incline.

Homework Equations





The Attempt at a Solution



I need to be given a mass to solve this! If I had a mass, I'd plug it into I = mr^2, find the inertia. With that, I'd plug it into E = mgh, and after i'd find W (angular velocity). Help!

The mass is m. You don't need to know the mass with this problem any more than you need to know the mass of an object to find its final speed after falling 2.5 meters, if it was released at rest.

Don't forget, the final Kinetic Energy, KE, includes a rotational part as well as a translational part, i.e. KE = (1/2)·I·ω2 + (1/2)·m·v2 .
 

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