The axle of a wheel is mounted on supports that rest on a rotating turntable as...

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The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 46. The wheel has angular velocity w₁ =44.0 rad/s about its axle, and the turntable has angular velocity w₂ = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) (a) What are the directions of 1 and 2 at the instant shown? (b) What is the resultant angular velocity of the wheel, as seen by an outside observer, at the instant shown? Give the magnitude and direction. (c) What is the magnitude and direction of the angular acceleration of the wheel at the instant shown? Take the z axis vertically upward and the direction of the axle at the moment shown to be the x axis pointing to the right. FIGURE 46 The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 46. The wheel has angular velocity w₁ =44.0 rad/s about its axle, and the turntable has angular velocity w₂ = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) (a) What are the directions of 1 and 2 at the instant shown? (b) What is the resultant angular velocity of the wheel, as seen by an outside observer, at the instant shown? Give the magnitude and direction. (c) What is the magnitude and direction of the angular acceleration of the wheel at the instant shown? Take the z axis vertically upward and the direction of the axle at the moment shown to be the x axis pointing to the right. FIGURE 46 The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 46. The wheel has angular velocity w₁ =44.0 rad/s about its axle, and the turntable has angular velocity w₂ = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) (a) What are the directions of 1 and 2 at the instant shown? (b) What is the resultant angular velocity of the wheel, as seen by an outside observer, at the instant shown? Give the magnitude and direction. (c) What is the magnitude and direction of the angular acceleration of the wheel at the instant shown? Take the z axis vertically upward and the direction of the axle at the moment shown to be the x axis pointing to the right. FIGURE 46

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Solution a The direction of the angular velocity vector of the wheel is shown in the figure as point... View the full answer