Question

Harry Potter (back to his normal size) has discovered that his magic wand is exactly one meter long. After some coaxing from Hermione, Harry is persuaded to mark off his wand in centimeters. Scabbers, the rat, (of mass 0.350 kg) is clinging tightly to the 70-cm mark of Harry's wand (of mass 0.100 kg.)Model Scabbers as a sphere of radius 5 cm. (He's put on a little weight lately.) as Hermionne rotates the wand in mid air, (as if on a horizontal, frictionless table) with an angular speed of 3.00 rad/s. Harry quickly calculates the moment of inertia and angular momentum of the wand-rat system when the wand is pivoted about an axis

(a) perpendicular to the plane of rotation through the 55.0-cm mark and

I = kg·m2

L = kg·m2/s

b) perpendicular to the plane of rotation through the 0-cm mark.

I = kg·m2

L = kg·m2/s

Answer 1

a) Distance of center of mass of scale from axis is

Distance of Scabbers from axis of rotation is

radius of Scabbers

Moment of inertia of scale about the axis ( at 55 cm) is

Moment of inertia of Scabbers about the axis of rotation is

Moment of inertia of system is

Angular momentum of system is

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b)

Distance of center of mass of scale from axis is

Distance of Scabbers from axis of rotation is

radius of Scabbers

Moment of inertia of scale about the axis ( at 0 cm) is

Moment of inertia of Scabbers about the axis of rotation is

Moment of inertia of system is

Angular momentum of system is

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