1) After doing some exercises on the floor, you are lying on your back with one

Question

1) After doing some exercises on the floor, you are lying on your back with one leg pointing straight up. If you allow your leg to fall freely until it hits the floor(Figure 1) , what is the tangential speed of your foot just before it lands? Assume the leg can be treated as a uniform rod 0.95 m long that pivots freely about the hip.

2) When the play button is pressed, a CD accelerates uniformly from rest to 500 rev/min in 3.0 revolutions. If the CD has a radius of 5.5 cm and a mass of 17 g , what is the torque exerted on it?

3) A fish takes the bait and pulls on the line with a force of 2.5 N . The fishing reel, which rotates without friction, is a uniform cylinder of radius 0.060 m and mass 0.99 kg. A)What is the angular acceleration of the fishing reel?. B) How much line does the fish pull from the reel in 0.25 s?

Explanation / Answer

Use conservation of energy to solve this. Let U (potential energy) be zero on the ground

So initially U = m*g*h where h = 0.475m (midpoint of the leg)

Now just before the leg hits it has K = 1/2*I*^2 where = v/r and I = 1/3*m*r^2

So m*g*h = 1/2*1/3*m*r^2*v^2/r^2 = 1/6*m*v^2

So v = sqrt(6*g*h) = sqrt(6*9.80*0.475) = 5.28m/s

2.Torque = I*
I = 1/2 * m * r^2 = 1/2 * 0.017 * 0.055^2 kg m^2

To find we can adjust Newton's equaiton of motion to circular motion
^2 = 0 + 2* *
(500*2/60)^2 = 2 * * 3*2
=72.72 rad/sec^2

Torque = 1.87 x 10^-3 Nm

3. I = mR^2/2 (moment of inertia of the reel)
M = RF (torque)
= / = 2F/mR = 5/(0.99*0.060) = 84.175 rad/s^2 (angular acceleration)
a = R = 5.05 m/s^2 (linear acceleration)
L = (1/2)at^2 = 0.5*5.05*.25 = .63125 m

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