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Microsoft PowerPoint - Knight Ch 12-Rotation of a Rigid Body notes

# Microsoft PowerPoint - Knight Ch 12-Rotation of a Rigid Body notes

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2 Rotational Kinematics Linear Motion Rotational Motion Position x Angular Position θ Velocity v Angular Velocity ω Acceleration a Angular acceleration α Table 13.1 Relation of Angular and Linear Quantities Looking at the tangential velocity of a point on the circle, we can define the velocity of that point as We can further the relationship by remembering that s=r θ , such that Where the derivative of the angular position is the angular velocity, ω dt ds v = dt d r dt ds v θ = = ω = r v Every point on the object has the same _________ speed, but not the same ____________ speed! ω r v = r ω ____________ Angular Velocity and Acceleration Figure 13.5 We derived the relationship between the linear and angular velocities. Taking the time derivative of this function Where the derivative of the angular velocity is the angular acceleration. Relation of Angular and Linear Quantities ω = r v dt d r dt dv a t ω = = α = r a t Only if the disk is speeding up or slowing down will there be a ______________ acceleration! α r a t = r α ____________ ____________
3 Rotation about the Center of Mass ... m m ... x m x m x m M 1 x 2 1 2 2 1 1 i i i cm + + + + = = ... m m ... y m y m y m M 1 y 2 1 2 2 1 1 i i i cm + + + + = = The center of mass is the mass-weighted center of the object. = xdm M 1 x cm = ydm M 1 y cm 13.10 Carpenters Square A carpenters square is 10 cm on each leg with a width of 4 cm. Find the center of mass of the square.

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Microsoft PowerPoint - Knight Ch 12-Rotation of a Rigid Body notes

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