Question

QUESTION 1 [13]

Suppose that due to a gravitational torque exerted by the Moon on the Earth, our planet's rotation slows at a rate of 1.30 ms/century (see picture below). Show the full calculations, including the conversions. Do not round up in intermediate calculations.

HINT: You will need to use basic definitions of: alpha, Δω, Δθ, and Δt to crack the problem.

(a) Calculate the Earth's angular acceleration due to this effect. (8)

(b) Calculate the torque exerted by the Moon on the Earth. (3)

(c) Calculate the length of the wrench / spanner an ordinary person would need to exert such a torque, as in the figure above. Assume the person can brace his feet against a solid firmament and exert a 850 N force. (2)

Answer 1

Answer:-

Given that due to torque exerted by the moon on the earth, The planet rotation slow at a rate of 1.3 ms/ century.

If 't' is the time taken to complete one rotation, then after a century, the time taken for one rotation will be as the rotating of planet is slowing down, it will take extra time for one rotation and hence will be the duration of day.

a)

We have time taken for one rotation of earth,

Present angular velocity of earth

After 100 year, time increase to

Angular velocity of earth after 100 years,

We have 100 years in second as

We know that

(-ve indicate angular deceleration as the rotation speed is slow down)

Therefore the angular acceleration due to this effect is

b)

Torque exerted by the moon on the earth

Assuming earth as a sphere , the moment of inertia from the earth fact sheet provided by NASA is obtained as

And mass of earth,

Volumetric radius of earth

  

Torque exerted by moon on the earth

C)

If the person exert f=850 N of force then the length of wrench can be optained from

Length of the wrench/ spanner

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