Physics 1001 Notes

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Unformatted text preview: r acceleration o a = atan + arad o Tangential acceleration: §༊ atan = dv dω =r = rα dt dt o Radial acceleration: §༊ arad v2 = = ω 2 r r Energy in Rotational Motion Kinetic energy in rotation • Consider a rigid body consisting of particles o Masses m1,m2,… at axial distances r1,r2… with the same wz=w o For a particle I with mass mi §༊ • 1 1 Ki = mi vi2 = mi (riω )2 2 2 The kinetic energy of the body is 1 k = ∑ mi r i2ω 2 2 1 2 2 o = (∑ mi ri )ω 2 12 o = Iω 2 2 where I = ∑ mi ri is the moment of inertia o • • • I is the rotational analog of mass Moment refers to the distribution of weight not a moment in time o The greater the distance from the axis to the particles that make up the body the greater the moment of inertia o The S.I unit is kg.m2 14 Physics 1001 Notes • For continuous distribution o • I= 2 ∫ r dm = ∫ r 2 pdV o dm=dV is a mass element at r o p, dV are density, volume of the element I depends on the rotation axis Parallel Axis Theorem • • Moment of inertia I depends on o Mass distribution o Axis of rotation Ip=ICoM+Md2 o Ip is parallel axis...
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This note was uploaded on 04/09/2014 for the course PHYS 1001 taught by Professor Helenjohnston during the Three '13 term at University of Sydney.

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