1) Determine the rotational acceleration of your arm at the start of your throw

Question

1)

Determine the rotational acceleration of your arm at the start of your throw if the muscle is relaxed.

2)A star the size of our Sun runs out of nuclear fuel and, without losing mass, collapses to a white dwarf star the size of our Earth. The radius of our Sun is 6.96×108m , the radius of Earth is6.37×106m .

If the star initially rotates at the same rate as our Sun, which is once every 25 days, determine the rotation rate of the white dwarf.

At the start of your throw of a 6.0-kg bowling ball, your arm is straight behind you and horizontal (Figure 1) Your arm is 0.64 m long, has a rotational inertia of 0.48 kg m2 and has a mass of 3.5 kg with its center o mass 0.28 m from your shoulder joint Figure 1of 1 CM 0.28 m AXis of rotation 0.64 m

Explanation / Answer

1. First we need to find net torque,

= F*r = 6.0kg * 9.8m/s² * 0.64m + 3.5kg * 9.8m/s² * 0.28m = 47.24 N·m

But = I *
Total I = 0.48kg·m² + 6.0kg * (0.64m)² = 2.94 kg·m²
so = / I = 47.24N·m /2.94kg·m² = 16.1 rad/s²

2.

Use law of conservation of angular momentum

Li = Lf

I(sun)wi =  I(earth)] wf

(2/5m1r1^2)wi =  (2/5m2r2^2)wf

But m1=m2= m

(2/5mr1^2)wi = (2/5mr2^2)wf

r1^2wi = r2^2wf

wf = wi*(r1^2/r2^2) = (1rev/25days)*[(6.96×108)^2/(6.37×106)^2] 477.5 rev/day

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