A rotating uniform-density disk of radius 0.8 m is mounted in the vertical plane

Question

A rotating uniform-density disk of radius 0.8 m is mounted in the vertical plane. The axle is held up by supports that are not shown, and the disk is free to rotate on the nearly frictionless axle. The disk has mass 5.4 kg. A lump of clay with mass 0.6 kg falls and sticks to the outer edge of the wheel at location A, < -0.76, 0.250, 0 > m. (Let the origin of the coordinate system be the center of the disk.) Just before the impact the clay has a speed 9 m/s, and the disk is rotating clockwise with angular speed 0.95 radians/s.

radians/s
(d) Qualitatively, what happens to the linear momentum of the combined system? (Think about why this is.)

The downward linear momentum decreases because the axle exerts an upward force.Some of the linear momentum is changed into angular momentum.    Some of the linear momentum is changed into energy.There is no change because linear momentum is always conserved.

Explanation / Answer

(A) for ball, Lball = m (r x v)

= 0.6 (-0.76i + 0.250j + 0k) x (-9j)

= 4.10 kg m^2 /s  

of diskL, Idisk =(5.4 x 0.8^2 / 2) (0.95)

= - 1.64 kg m^2 / s

Li = 2.46kg m^2 / s

(b) from angular momentum conservation,  

Lf = Li = 2.46 kg m^2 /s

(c) LF = I w

2.46 = ((5.4 x 0.8^2 / 2) + (0.6 x 0.8^2)) w

w = 1.16 rad/s

(d) The downward linear momentum decreases because the axle exerts an upward force

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

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