Rev. 2 REVIEW SHEET #8: Rolling Motion Rolling motion combines translational motion of an object’s center of mass and rotational motion about an axis passing through the center of mass. The linear acceleration of the center of mass is determined by Newton’s Second Law for Translational Motion : ext cm F Ma = ∑ r r (M = the total mass of the object) The angular acceleration of the object about an axis through the center of mass is determined by Newton’s Second Law for Rotational Motion : ext I τ α = ⋅ ∑ r r The latter equation is valid provided the following conditions are met: (1) The axis through the center of mass must be an axis of symmetry; (2) The axis must not change direction. If the object rolls without slipping , the relationships between the linear and angular kinematic variables (see Review Sheet #6) apply: s r θ = ( in radians), r v ϖ = and tan r a = Use them to reduce the number of unknowns involved in a problem. Hints for solving problems involving a single rolling object (e.g., Problems #9 and #11
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