Gravitational potential energy:
Moment of inertia of a sphere:
Rotational kinetic energy:
Translational kinetic energy:
We'll use trigonometry to determine the height of the incline.
sinθ = h/L
h = Lsinθ
The gravitational potential energy of the sphere is converted into kinetic energy of the sphere.
U = Krot + Ktranslational
An 8.0 cm diameter, 400 g sphere is released from rest at the tip of a 2.1 m long, 25 degree incline. It rolls, without slipping, to the bottom.
What is the sphere's angular velocity at the bottom of the incline?
Frequently Asked Questions
What scientific concept do you need to know in order to solve this problem?
Our tutors have indicated that to solve this problem you will need to apply the Conservation of Energy in Rolling Motion concept. You can view video lessons to learn Conservation of Energy in Rolling Motion. Or if you need more Conservation of Energy in Rolling Motion practice, you can also practice Conservation of Energy in Rolling Motion practice problems.