A uniform disk of mass 0.80 kg and radius 5.6 cm is mounted in the center of a 1

Q: A uniform disk of mass 0.80 kg and radius 5.6 cm is mounted in the center of a 1

a) wp = M * g * D / Is * ws Is = 0.5 * m * R^2 wp = 2*g*D /(R^2 *ws) then wp = 2 * 9.8 * 0.05 / (0.056^2 * 800 * 2 * pie/60) wp = 3.73 rad/s b) Vcm = wp * D Vcm = 3.73 * 0.05 = 0.1865 m/s c) acm = D * wp^2 acm = 0.695 m/s^2 d) Fv = M*g Fh = M*acm Fv = 0.8 * 9.8 = 7.84 N Fh = 0.8 * 0.695 = 0.556 N

ID: 1350829 • Letter: A

Question

A uniform disk of mass 0.80 kg and radius 5.6 cm is mounted in the center of a 10 cm axle and spun at 800 rev/min. The axle is then placed in a horizontal position with one end resting on a pivot. The other end is given an initial horizontal velocity such that the precession is smooth with no nutation.

(a) What is the magnitude of the angular velocity of precession?
_______rad/s

(b) What is the speed of the center of mass during the precession?
________m/s

(c) What are the magnitude and direction of the acceleration of the center of mass?
________m/s2

(d) What is the magnitude of the vertical component of the force exerted by the pivot?
_________N
What is the horizontal component?
_________N

Explanation / Answer

wp = M * g * D / Is * ws

Is = 0.5 * m * R^2

wp = 2*g*D /(R^2 *ws)

then

wp = 2 * 9.8 * 0.05 / (0.056^2 * 800 * 2 * pie/60)

wp = 3.73 rad/s

Vcm = wp * D

Vcm = 3.73 * 0.05 = 0.1865 m/s

acm = D * wp^2

acm = 0.695 m/s^2

Fv = M*g

Fh = M*acm

Fv = 0.8 * 9.8 = 7.84 N

Fh = 0.8 * 0.695 = 0.556 N

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A uniform disk of mass 0.80 kg and radius 5.6 cm is mounted in the center of a 1

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A uniform disk of mass 0.80 kg and radius 5.6 cm is mounted in the center of a 1

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