The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in the figure.(Figure 1) The wheel has angular velocity ω1 ω 1 = 44.0 rad/s r a d / s about its axle, and the turntable has angular velocity ω2 ω 2 = 37.5 rad/s r a d / s about a vertical axis. (Note arrows showing these motions in the figure.) Take the z z axis vertically upward and the direction of the axle at the moment shown to be the x x axis pointing to the right. Take the direction perpendicular to that of the axle at the moment shown to be the y y axis pointing in the page.
a) What are the directions of ω⃗1 at the instant shown?
b) What are the directions of ω⃗2 at the instant shown?
c) What is the resultant angular velocity of the wheel, as seen by an outside observer, at the instant shown? Give the magnitude.
d) Give the angle of the resultant angular velocity of the wheel.
e) What is the magnitude of the angular acceleration of the wheel at the instant shown?
f) What is the direction of the angular acceleration of the wheel at the instant shown?