Question

1 2 3 4 56 A uniform disk of mass 0.76 kg and radius 5.7 cm is mounted in the center of a 10 cm axle and spun at 795 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. 1) (a) What is the magnitude of the angular velocity of precession? rad/s Submit You currently have 0 submissions for this question. Only 7 submission are allowed You can make 7 more submissions for this question 2) (b) What is the speed of the center of mass during the precession? m/s Submit You currently have O submissions for this question. Only 7 submission are allowed You can make 7 more submissions for this question 3) (c) What are the magnitude and direction of the acceleration of the center of mass? m/s2 Submit You currently have O submissions for this question. Only 7 submission are allowed You can make 7 more submissions for this question 4) horizontally toward the pivot point in the direction of rotation of the disk in the direction of precession of the disk Submit You currently have 0 submissions for this question. Only 7 submission are allowed. You can make 7 more submissions for this question 5) (d) What is the magnitude of the vertical component of the force exerted by the pivot? N Submit You currently have O submissions for this question. Only 7 submission are allowed. You can make 7 more submissions for this question.

Answer 1

(1)

w1 = 795 rev/min = 83.252 rad/s

Angular momentum, L = l*w

L = (1/2)mR^2 * w1

L = (1/2)*0.76*0.057²*83.252 = 0.1027

w2 = mgd / L

w2 = 0.76*9.8*(0.10 / 2) /  0.1027

w2 = 3.623 rad/s

(2)

Speed of center of mass,

v = w*d

v =  3.623 * 0.05

v = 0.18115 m/s

(3)

Acceleration of center of mass,

a = w^2*d

a = (3.623)^2 * 0.05

a = 0.6563 rad/s^2

(4)

Direction is horizontal towards the pivot point.

(5)

Vertical component of force,

Fv = mg

Fv = 0.76*9.8

Fv = 7.448 N

(6)

Horizontal component of force,

Fh = ma

Fh = 0.76* 0.6563

Fh = 0.4987 N