(II) The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 10–46. The wheel has angular velocity ω 1 = 44.0 rad/s about its axle, and the turntable has angular velocity ω 2 = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) ( a ) What are the directions of ω → 1 and ω → 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.
(II) The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 10–46. The wheel has angular velocity ω 1 = 44.0 rad/s about its axle, and the turntable has angular velocity ω 2 = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) ( a ) What are the directions of ω → 1 and ω → 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.
(II) The axle of a wheel is mounted on supports that rest on a rotating turntable as shown in Fig. 10–46. The wheel has angular velocityω1 = 44.0 rad/s about its axle, and the turntable has angular velocity ω2 = 35.0 rad/s about a vertical axis. (Note arrows showing these motions in the figure.) (a) What are the directions of
ω
→
1
and
ω
→
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.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
A small mass m on a string is rotating without friction in acircle. The string is shortened by pulling it through the axisof rotation without any external torque, Fig. 8–39. Whathappens to the tangential velocity of the object?(a) It increases.(b) It decreases.(c) It remains the same.
A wheel with moment of inertia, I = (3⁄4) mR2 of radius 0.50 m and a mass of 0.30 kg is releasedfrom rest and allowed to roll down an inclined plane. How fast is it moving after dropping a verticaldistance of 3.8 m?
whaT magnitude of (constant) force appliedhorizontally at the axle of thewheel is necessary to raise the wheelover a step obstacle of heighth = 3.00 cm? The wheel’s radius is r =6.00 cm, and its mass is m= 0.800 kg.
Chapter 10 Solutions
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