1. You are a science consultant to a sci-fi movie director who wants the Earth t

Question

1. You are a science consultant to a sci-fi movie director who wants the Earth to experience a torque that will cause the Earth's rotation to slow down so that its new period will be 36 hours long. The torque acts over a time period of 24 hours. Model the Earth as a uniform solid sphere rotating about its axis for its moment of inertia and that the force producing the torque is tangent to the Earth's equator. You'll need to look up the Earth's mass and radius.

      (a) What are the initial and final angular velocities of the Earth?

      (b) What is the angular deceleration of the Earth?

      (c) What is the magnitude of the force needed to slow the Earth?

Two disks are to be made into an idealized clutch. Disk 1 has a mass of 3.00 kg and a radius of 20.0 cm, while disk 2 has a mass of 1.00 kg and a radius of 20.0 cm. If disk 2 is originally at rest and disk 1 is rotating at 2000 rpm, what is the final angular velocity of the coupled disks?

Explanation / Answer

angular velocity of earth

w = 2pi/T

initial T = 24hours R = radius of earth = 6371000m

wi = 2*pi/24*60*60 = 7.26*10^-5 rad/s

final Wf = 2*pi/36*60*60 = 4.84*10^-5rad/s

part b

angular decceleration

a = wf-wi/t

t = 24 hours

a = 2.80*10^-10rad/s^2

part c

magnitude of force

torque = I*a= F*R

F = I*a/R

I =2/5MR^2

F = 2*M*R/5*a

F = 2*5.9*10^24*6371000/5*2.8*10^-10

F = 5.36x10^40 N

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

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