(4) Two ballerinas of different heights must perform a move where they spin on o

Question

(4) Two ballerinas of different heights must perform a move where they spin on one leg while other leg parallel to the ground. One ballerina is 1.6 m tall and extends her leg 0.8 m from her body while the other ballerina is 1.7 m tall and extends her leg 0.9 m from her body. For the sake of art, they must synchronize so that they spin at the same rate of 1.5 rev/s (a) What is the centripetal acceleration of each ballerina's extended foot? Give your answer in m/. (b) After each completing 3 revolutions, the two ballerinas coordinate pulling their foot inward, leaving their knee as the furthest point revolving. Their knee extends half as far from their body as their foot did. If they maintain the same centripetal acceleration on their knees as they did on their feet, at wha they rotating? Give your answer in rev/s t rate are (c) What is the relationship between the initial angular velocity and the final angular velocity? There should be a simple way to find the answer to (b) without needing nuch calculation. (5) A man with very complicated shoes is holding a pocket wateh. At noon, he makes the astute observation that the hour hand and minute hand line up exactly. When is the next time T he will be able thrill of seeing them meet up again? Give your answer in the form: hh:mmss

Explanation / Answer

(a)We know that the centripital acceleration is given by:

ac = v^2/R ; v = R w ;

ac = R^2 w^2/R = w^2 R

w = 1.5 rev/s = 9.4 rad/s

ac1 = 9.4^2 x 0.8 = 70.7 m/s^2

ac2 = 9.4^2 x 0.9 = 79.5 m/s^2

Hence, ac1 = 70.7 m/s^2 ; 79.5 m/s^2

b)3 rev = 18.85 rad

We know that

w^2 = w0^2 + 2 alpha theta

alpha1 = 70.7/0.8 = 88.4 rad/s^2

alpha2 = 88.3 rad/s^2

w^2 = 9.4^2 + 2 x 88.4 x 18.85 = 58.5 rad/s

Hence, w = 58.5 rad/s

c)The final angular velocity is more than initial angular velocity.

Yes the more simpler way could be conservation of angular momentum, but the information is less for calculating the moment of inertia.

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

---

---

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