# Mastering Physics 9

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 the same as the angular speed of ladybug 2 What is the angular speed of ladybug 1? one-half the angular speed of ladybug 2 the same as the angular speed of ladybug 2 twice the angular speed of ladybug 2 one-quarter the angular speed of ladybug 2 2 What is the ratio of the linear speed of ladybug 2 to that of ladybug 1? 2 What is the ratio of the magnitude of the radial acceleration of ladybug 2 to that of ladybug 1? +z What is the direction of the vector representing the angular velocity of ladybug 2? See the figure for the directions of the coordinate axes. +x −x +y −y +z −z −y Now assume that at the moment pictured in the figure, the disk is rotating but slowing down. Each ladybug remains "stuck" in its position on the disk. What is the direction of the tangential component of the acceleration (i.e., acceleration tangent to the trajectory) of ladybug 2? +x −x +y −y +z −z true True or false: The quantity represented by θ is a function of time (i.e., is not constant). true false false True or false: The quantity represented by θ0 is a function of time (i.e., is not constant). true false false True or false: The quantity represented by ω0 is a function of time (i.e., is not constant). true false true True or false: The quantity represented by ω is a function of time (i.e., is not constant). true false ω2=ω20+2α(θ−θ0) Which of the following equations is not an explicit function of time t? Keep in mind that an equation that is an explicit function of time involves t as a variable. θ=θ0+ω0t+12αt^2 ω=ω0+αt ω2=ω20+2α(θ−θ0) the time elapsed from when the angular velocity equals ω0 until the angular velocity equals ω In the equation ω=ω0+αt, what does the time variable t represent? Choose the answer that is always true. Several of the statements may be true in a particular problem, but only one is always true. the moment in time at which the angular velocity equals ω0 the moment in time at which the angular velocity equals ω the time elapsed from when the angular velocity equals ω0 until the angular velocity equals ω θB(t)=θ0+1/2ω0(t−t1)+α(t−t1)^2 Which of the following equations describes the angular position of particle B? θB(t)=θ0+2ω0t+14αt^2 θB(t)=θ0+1/2ω0t+αt^2 θB(t)=θ0+2ω0(t−t1)+1/4α(t−t1)^2 θB(t)=θ0+1/2ω0(t−t1)+α(t−t1)^2 θB(t)=θ0+2ω0(t+t1)+1/4α(t+t1)^2 θB(t)=θ0+1/2ω0(t+t1)+α(t+t1)^2 (ω0+2αt1)/2α How long after the time t1 does the angular velocity of particle B equal that of particle A? ω0/4α (ω0+4αt1)/2α (ω0+2αt1)/2α The two particles never have the same angular velocity. ma/mb = 0.333 Find the ratio of the masses of the two balls. da = 3L/4 Find da, the distance from ball a to the system’s center of mass. C=F>B>A=E>D Rank the moments of inertia of this object about the axes indicated. Router = 0.6 m R inner = 0.5 m > Router = 0.4 m R inner = 0.3 m > Router = 0.8 m R inner = 0.4 m = Router = 0.4 m R inner = 0.2 m = Router = 0.2 m R inner = 0.1 m > Router = 0.6 m R inner = 0.2 m Rank these scenarios on the basis of the linear speed of the block: Router = 0.6 m R inner = 0.5 m, Router = 0.4 m R inner = 0.3 m, Router = 0.8 m R inner = 0.4 m, Router = 0.4 m R inner = 0.2 m, Router = 0.2 m R inner = 0.1 m, Router = 0.6 m R inner = 0.2 m E =B > C > F=A > D Rank the designated points on the basis of their linear or tangential speed. B > C > F > A=D=E Rank the designated points in (Figure 2) on the basis of the magnitude of their linear or radial acceleration. B > C > A=F> D=E Rank these graphs on the basis of the angular velocity of each object. Rank positive angular velocities as larger than negative angular velocities. A=B=C=D=E=F Rank these graphs on the basis of the angular acceleration of the object. Rank positive angular accelerations as larger than negative angular accelerations.

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