Apt 9, 2018 Third 5 of 6 Name 4. The following questions (parts) are to be consi

Question

Apt 9, 2018 Third 5 of 6 Name 4. The following questions (parts) are to be considered independent questions to be an- swered as stand alone probles (1) (10 points) Calculate the angular velocity of a grandfather's clock second and minute hand in radys and rpm (u) (10 poitnts) If the Earth's day were to get shorter by 86.4s, how much faster would a person in Earth's equator move around the Earth, as it rotates around its axis? (Radius of Earth 6371km.) (au) (1o points) If we consider Earth a sphere, how much rotational kinetic energy does it have fron rotating around its own axis? (Mass of Earth = 5.972 × 1024kg.)

Explanation / Answer

angular velocity of second hand = angle / time = 2*pi / 60 = 0.1047 rad/s and rpm = 60 rpm

angular velocity of minute hand = angle / time = 2*pi / 3600 = 0.001745 rad/s and rpm = 1 rpm

_

actual length of day = 24*3600 = 86400s, so angular speed = 2*pi/86400 = 7.27*10^-5 /s

new length of day = 86400-86.4 = 86313.6s , so angular speed = 2*pi/86313.6 = 7.28*10^-6 /s

So, a person on equator would move faster by a speed of = radius of earth in m*(difference in angular velocities) = 0.4638m/s

_

Moment of inertia of earth = I = 2mr^2/5 = 2*5.972*10^24*6371000^2/5 = 9.696*10^37 kgm^2

Angular velocity = w = 2*pi/ 24*3600 = 7.27*10^-5 /s

So, kinetic energy in rotating around its own axis = 0.5Iw^2 = 2.56*10^29J

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

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