How Is Rotational Kinetic Energy Calculated for a Cylinder Rolling Down a Ramp?

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SUMMARY

The calculation of rotational kinetic energy for a cylinder rolling down a ramp involves using the correct formula for rotational inertia. The moment of inertia for a solid cylinder is given by I = 1/2 mr^2, not I = 2/5 mr^2, which is applicable to a rolling ball. The total kinetic energy (KE) is calculated using KE = 1/2 mv^2 + 1/2 Iω^2, where ω is the angular velocity. The conservation of energy principle mgh = KE must be applied correctly to find the velocity before substituting it into the kinetic energy equations.

PREREQUISITES
  • Understanding of rotational inertia and its formulas
  • Familiarity with the conservation of energy principle
  • Basic knowledge of angular velocity and its relationship to linear velocity
  • Ability to perform calculations involving mass, height, and radius
NEXT STEPS
  • Study the moment of inertia for different shapes, particularly solid cylinders
  • Learn how to derive angular velocity from linear velocity
  • Explore the conservation of energy in rotational motion
  • Practice problems involving rolling objects and their kinetic energy calculations
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Physics students, educators, and anyone interested in understanding the dynamics of rolling motion and energy conservation principles in mechanics.

map7s
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A 2.4 kg cylinder (radius = 0.09 m, length = 0.50 m) is released from rest at the top of a ramp and allowed to roll without slipping. The ramp is 0.74 m high and 5.0 m long. What is its rotational kinetic energy?

I just wanted to make sure that I was on the right track...

I=2/5 mr^2
KE=1/2 mv^2 + 1/5 mv^2

Using conservation of energy: mgh=1/2 mv^2 + 1/5 mv^2 and then solve for v and plug into equation for KE.

Does this sound like I'm doing this correctly?
 
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map7s said:
I just wanted to make sure that I was on the right track...

I=2/5 mr^2
KE=1/2 mv^2 + 1/5 mv^2
You are on the right track, but you are using the wrong formula for rotational inertia. (2/5 mr^2 is for a rolling ball, not a cylinder.)
 

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