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# lecture28 - Rolling Motion Combined translational and...

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Physics 1D03 Rolling Motion Rolling Motion Combined translational and rotational motion “Rolling without slipping” Dynamics of rolling motion Serway & Jewett: 10.9

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Physics 1D03 General Motion of a Rigid Body = 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 any stationary axis of rotation). Kinetic energy: 2 2 1 2 2 1 ϖ CM CM rot trans I mv K K K + = + =
Physics 1D03 Different points on a rolling object have different velocities (blue vectors). The velocity of each particle (blue) is the velocity of the centre (red) plus the velocity r ϖ relative to the centre (green): v = v CM + The point in contact with the ground is momentarily stationary. The point on the top of the wheel moves forward at twice the speed of the centre. C Rolling Motion v C ϖ

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Physics 1D03 If the body rolls without slipping, then its angular velocity and angular acceleration are related to the linear velocity and tangential
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