A solid disk rotates in the horizontal plane at an angular velocity of 0.027 rad
ID: 1353063 • Letter: A
Question
A solid disk rotates in the horizontal plane at an angular velocity of 0.027 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.15 kg · m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk? A solid disk rotates in the horizontal plane at an angular velocity of 0.027 rad/s with respect to an axis perpendicular to the disk at its center. The moment of inertia of the disk is 0.15 kg · m2. From above, sand is dropped straight down onto this rotating disk, so that a thin uniform ring of sand is formed at a distance of 0.40 m from the axis. The sand in the ring has a mass of 0.50 kg. After all the sand is in place, what is the angular velocity of the disk?Explanation / Answer
Apply law of conservation of angular momentum
I1*w1 = I2*w2
(0.15*0.027) = (0.15+M*r^2)*w2
(0.15*0.027) = (0.15+ 0.5*0.4*0.4)*w2
w2 = 0.0176 rad/s
Related Questions
Hire Me For All Your Tutoring Needs
Integrity-first tutoring: clear explanations, guidance, and feedback.
Drop an Email at
drjack9650@gmail.com
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.