Revolutions of a Sphere on an Incline

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SUMMARY

The discussion focuses on calculating the number of revolutions a sphere makes while rolling down an incline. The sphere, with a radius of 0.19 meters, starts from a height of 7 meters on a 36-degree incline. The length of the incline is determined to be 11.91 meters using the formula x = height/sin(angle). The next step involves applying the conservation of energy principle to find the sphere's final velocity and subsequently the number of revolutions.

PREREQUISITES
  • Understanding of basic physics concepts such as conservation of energy
  • Knowledge of rotational motion and moment of inertia
  • Familiarity with trigonometric functions, specifically sine
  • Ability to perform calculations involving linear and angular displacement
NEXT STEPS
  • Apply conservation of energy to determine the sphere's final velocity at the bottom of the incline
  • Calculate the moment of inertia for a solid sphere
  • Determine the angular velocity from the linear velocity using the relationship between them
  • Calculate the number of revolutions using the formula for angular displacement
USEFUL FOR

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

yankeekd25
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Homework Statement


A sphere of radius 0.19 meters starts from rest at the top of an incline at a height of 7 meters. The angle of the incline is 36 degrees. How many revolutions does the sphere make as it rolls to the end of the incline without slipping?
 
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You need to post an attempt. Start by finding the distance the sphere must roll.
 
rock.freak667 said:
You need to post an attempt. Start by finding the distance the sphere must roll.

x (length of incline)= 7/ sin 36 = 11.91 m.

What is the next step please? Do I need to do something with conservation of energy?
 

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