torque wrench bits

torque wrench bits
Torque and Acceleration!!!!:)?

Suppose that due to a gravitational torque exerted by the Moon on the Earth, our planet's rotation slows at a rate of 2.60 ms/century.

(a) Calculate the Earth's angular acceleration due to this effect.
________rad/s^2

(b) Calculate the torque exerted by the Moon on the Earth.
________N*m

(c) Calculate the length of the wrench an ordinary person would need to exert such a torque, as in Figure P10.67. Assume the person can brace his feet against a solid firmament and exert a 800 N force.
________m

****I'm having a bit of trouble with solving this problem; please help? Will rate handsomely:)

A. The angular acceleration is the rate of change in angular velocity.
The angular velocity of the earth is V = 2pi/24hours.
24 hours is the period of rotation.
Converting to radians/sec, V = 2pi/(24*60*60) = 2pi/86400= 7.27/10^5
Due to the moon, the period lengthens by 2.6 milli seconds per century.
Convert this to seconds/seconds: 2.6/(1000*100*365.25*24*60*60) = 8.24/10^13
So after 1 second, the angular velocity is V1 = 2pi/(86400+8.24/10^13)
Angular acceleration is A = V1-V = 2pi/(86400+8.24/10^13) - 2pi/86400
= 2pi * (18.24/10^13)/(86400 * (86400+8.24/10^13))
= 1.54/10^21 radians/second^2

B. Torque = IA, I is the moment of inertia and A is the angular acceleration.
I = (2/5) mr^2
where
m is the mass of the earth = 5.9742 × 10^24kg
r is the radius of the earth = 6.38*10^6 meters
Torque=(2/5) * 5.9742 * 10^24 * (6.38*10^6)^2 * 1.54/10^21
= (2/5) * 5.9742 * 1000 * (6.38*10^6)^2 * 1.54
= 1.50 * 10^17 Newton meters.

C. 800 * L = 1.50 * 10^17
L = 1.50 * 10^17/800=1.88 * 10^14 meters.

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