4. A figure skater goes into a spin, keeping her arms up and close to her body,

Question

4. A figure skater goes into a spin, keeping her arms up and close to her body, illustrating conservation of angular momentum. In a classroom demonstration of the above effect, a student is standing on a rotating platform, which is spinning with 2 rev/s . The student is holding two heavy dumbbells, 5 kg each, originally tightly pressed to his/her body at a negligible distance from the axis of rotation The student then extends the arms horizontally, bringing each dumbbell 80 cm from the axis of rotation. Assume the student (without dumbbells) and the platform have a combined rotational inertia of I 8kg m2 and (unlike the case of the figure skater) neglect the rotational inertia of extended arms (a) find the original w (b) find the angular momentum L (c) find the final I' (note: there are two arms) (d) find the final (e) find the change in kinetic energy 5. A merry-go-round on a playground has rotational inertia I = 50 kg·m2 and is spinning at w = 2 rad/s. An m = 30 kg kid hops on the platform, 1 m away from the axis of rotation, with no initial velocity. (a) find the new rotational inertia I' (b) Find the new angular velocityu. 6. An M = 2 kg disk with R = 1 m is freely spinning with w = 4 rad/s. A ring with m = 0.5 kg, r = 80 crn is dropped onto the center of the dsk and sticks to it. Find the new (in rad/s).

Explanation / Answer

4. (A) w = 2 rev/s = 2 x 2 pi rad/s

w = 12.6 rad/s

(B) L = I w = 8 x 12.6 = 100.5 kg m^2 / s

(C) I' = 8 + 2(5 x 0.80^2) = 14.4 kg m^2

(d) Lf = I'w ' = 100.5

w' = 7 rad/s

(e) Ki = (8 x 12.6^2 / 2) = 635.04 J  

Kf = 14.4 x 7^2 /2 = 352.8 J  

change in KE = Kf - Ki = - 282.24 J

Related Questions

Navigate

• Browse (All)
• Browse 4
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.