# lecture30 - 1 Physics 1D03 2 Rolling Motion Rolling Motion...

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Unformatted text preview: 1 Physics 1D03 2 Rolling Motion Rolling Motion • Combined translational and rotational motion • “Rolling without slipping” • Dynamics of rolling motion Text Section : 10.9 Practice problems: Chapter 10, problems 53, 55, 83 Physics 1D03 3 The general motion of a rigid body ( i.e. , not pure rotation about a fixed axis) can be described as translation of the center of mass, plus rotation about the center of mass. Kinematics ( ) ( ) ( ) t t t CM CM CM a v r Refer to motion of center of mass ( ) ( ) ( ) → , , t t t α ω θ Refer to rotation about an axis though the center of mass, which travels with the center of mass ( ) t v y ( ) t v x a CM = g ω CM v CM 2 Physics 1D03 4 Dynamics ∑ = CM a F m ∑ = α τ I CM CM Gives linear acceleration of the position of the center of mass. Gives angular acceleration of the body about the center of mass. These are special properties of the centre of mass only (although τ = Ια is also true for a stationary axis of rotation). Kinetic energy: 2 2 1 2 2 1 ω CM CM rot trans I mv K K K + = + = Physics 1D03 6 Different points on a rolling object have different velocities (blue vectors). The velocity of each...
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lecture30 - 1 Physics 1D03 2 Rolling Motion Rolling Motion...

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