http://s10.postimg.org/pwi0mdhd5/image.gif A sphere of mass m and radius r is at

Question

http://s10.postimg.org/pwi0mdhd5/image.gif

A sphere of mass m and radius r is attached to the rim of a disk (mass M, radius R). The disk is rotating counter-clockwise with a constant period T around an axis through the center of the disk. Neglect friction. Consider the directions A through I at the indicated position of the sphere.

1. What is the direction of the external torque on the disk?

2. What is the direction of the net force on the sphere?

3. What is the direction of the acceleration of the sphere?

4. If the disk has a radius R=0.5 m and a mass M=0.9 kg, and the sphere has a radius r=0.02 m and a mass m=0.28 kg, and if the period of rotation is T=5 s, what is the magnitude of the angular velocity of the disk?

5. What is the magnitude of the velocity of the sphere?

6. What is the moment of inertia of the whole contraption around the axis through the center of the disk?

I (disk,cm) = (1/2)MR^2                     I(sphere,cm) = (2/5)mr^2

7. Now, the disk is accelerated counter-clockwise to spin faster. What is the direction of the external torque?

8. While the disk is spun up, what is the direction of the acceleration of the sphere?

9. The sphere was not glued on very well and disconnects. In what direction is it going to fly off?

Explanation / Answer

1) Zero , No external torque.

2) Along F, the centripetal force

3) Acceleration is also along the center so Along F

4) w = 2 pi / T = 2 * 3.14 /5 = 1.257 rad/s

5) v = 2*pi*R/T = 2*3.14*0.3/5 = 0.377 m/s

6) I = Idisk,cm + Isphere,cm + m*R^2

    I = 0.5*M*R^2 + (2/5)*m*r^2 + m*R^2

     I = 0.183 kg.m^2

7) Along I, upward

8) Along B, outward

9) Along A

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.