Kinetic energy of rotating and rolling bodies.pptx

Kinetic energy of rotating and rolling bodies in Mechanics

1. KE of rotating and rolling bodies

2. A B ω P C r v M m

3. When ω =1 unit,

4. Rolling bodies

5. Rolling bodies A body with circular symmetry like cylinder, wheel, disc , sphere translational + rotational motion v v + v=R ω -v=-R ω 2v P

6. Rolling bodies 2v P MI about the axis through P O MI about a parallel axis through O k=Radius of gyration

7. θ potential energy = Mgh s h Motion in Inclined plane

8. A sphere, a cylinder, and a hoop, all of mass M and radius R, are released from rest and roll down a ramp of height h and slope θ.

9. A 1.20 kg disk with a radius 0f 10.0 cm rolls without slipping. The linear speed of the disk is v = 1.41 m/s. (a) Find the translational kinetic energy (b) Find the rotational kinetic energy. (c) Find the total kinetic energy.