Claire sits on a bar stool, with her feet off of the floor. The seat of the bar
ID: 2264665 • Letter: C
Question
Claire sits on a bar stool, with her feet off of the floor. The seat of the bar stool is free to rotate. Claire is holding a wheel (moment of inertia = 1.94 kg m2) that is spinning counterclockwise at an angular speed of 18.80 rad/s, as shown below. Claire and the bar stool are stationary. (Claire + the bar stool have a moment of inertia of 51.80 kg m2.) Claire, being adventurous, flips the axle of the wheel by 180o (applying an internal torque) and holds the wheel in place. What happens to Claire and the wheel?
(a) What is "the system" for this problem?
(b) What is the total angular momentum of the system?
Magnitude kg m2/s
Direction (One Submission)
(c) What is the angular momentum of the wheel after Claire flips it over?
Magnitude kg m2/s
Direction (One Submission)
(d) What is (the bar stool + Claire)`s angular momentum after Claire flips the wheel over?
Magnitude? kg m2/s
Direction? (One Submission)
(e) What is Claire`s angular velocity after she flips the wheel over?
Magnitude? rad/s
Direction? (One Submission)
Explanation / Answer
Claire sits on a bar stool, with her feet off of the floor. The seat of the bar stool is free to rotate. Claire is holding a wheel (moment of inertia = 1.87 kg m2) that is spinning counterclockwise at an angular speed of 17.80 rad/s, as shown below. Claire and the bar stool are stationary. (Claire + the bar stool have a moment of inertia of 51.80 kg m2.) Claire, being adventurous, flips the axle of the wheel by 180o (applying an internal torque) and holds the wheel in place. What happens to Claire and the wheel?
<p>a)The wheel, Claire, and the bar stool.<br /><br />b) UP (counterclockwise)<br />angular momentum is constant = Iω<br />= 1.87 x 17.80<br />=33.286</p>
<p>c) when the wheel is fillped by 180 degrees, the angular momentum of wheel becomes in clockwise direction.</p>
<p>Hence it will be in the downward direction with same magnitude 33.286 kg-m<sup>2</sup>/s</p>
<p>d)</p>
<p>Since the angular momentum of the system remains constant.</p>
<p>Hence L<sub>claire &stool</sub> + L<sub>wheel final</sub>= L <sub>wheel initial</sub></p>
<p>or  L<sub>claire &stool</sub> + ( -33.286) = 33.286</p>
<p>∴ L<sub>claire &stool</sub> = 33.286 *2 = 66.572 kg-m<sup>2</sup>/s</p>
<p>Claire & stool will rotate with same ngular velocity. Let it be ω<sub>c</sub></p>
<p>hence I<sub>c</sub> * ω<sub>c</sub> = 66.572 kg-m<sup>2</sup>/s</p>
<p> I<sub>c</sub> = 51.8 kg-m<sup>2</sup></p>
<p>Hence ω<sub>c</sub> = 66.572/ 51.8 = 1.285 rad/s = 1.29 rad/sec ≈</p>
<p>hope this will do. :)</p>