A gramophone record consists of a uniform circular disk of radius R and total mass M with a hole punched through it's center with a radius r.
a) Show that the moment of inertia of the record about the perpendicular axis passing through it's center is 1/2 M(R^2 + r^2).
b)A gramophone record having a mass of m=100g, radius =15cm and hole of radius 3cm is rotating freely on a turntable at 33 revolutions per minute with no friction. A point mass of 10g is dropped onto the record at a distance of 10cm from it's center and sticks to the point of impact. Calculate the new speed of rotation of the record
A gramophone record consists of a uniform circular disk of radius R and total mass M...
A turntable has a radius R and mass M (considered as a disk) and is rotating at an angular velocity W 0 about a frictionless vertical axis. A piece of clay is tossed onto the turntable and sticks d from the rotational axis. The clay hits with horizontal vel ocity component vc at right angle to the turntable’s radius, and in a direction that opposes the rotation. After the clay lands, the turntable has slowed to angular velocity W1 ....
A disk with uniform density and radius 0.596 m used to weigh 24.48 kg, but then a hole was punched out. The black arrow in the image above shows the axis of rotation. The hole has radius 0.0951 m, and has its center 0.164 m away from the center of the disk. What is the moment of inertia of the disk with a hole? (Hint: only a scientist could call a hole negative mass! Find the mass taken away based...
A uniform disk with mass M and radius R is rotating about an axis through its center-of-mass. The axis is perpendicular to the disk. The moment of inertial for the disk with a central axis is I MR2. Two non-rotating smaller disks, each with mass M2 and radius R/4, are glued on the original disk as shown in the figure. (a) Show that the ratio of the moments of inertia is given by I'/I = 35/16, where I' is the moment...
A uniform solid disk of mass m = 3.06 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.09 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim?...
Imagine a spinning disk of uniform density, with mass M and radius R. Except where noted, it is rotating about an axis through its center and perpendicular to its plane. What is its moment of inertia if the axis of rotation is moved to a line 2R from the center of the disk? (There’s no rotation of the axis, it remains parallel to its original position). Could someone explain what this question is asking in a diagram?
A uniform solid disk of mass m = 3.08 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.09 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim?...
A uniform solid disk of mass m = 2.99 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 5.96 rad/s. (a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass. kg · m2/s (b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim?...
specify equations used please
Part I: A disk of mass M and radius R is rotating with some angular velocity o, about a frictionless axis. A non rotating solid hemisphere of radius R is to be dropped from above and it sticks to the lower disk so that the new angular velocity is 1/3 0.. What is the mass of the hemisphere in terms of M?
A particular horizontal turntable can be modeled as a uniform disk with a mass of 180 g and a radius of 30.0 cm that rotates without friction about a vertical axis passing through its center. The angular speed of the turntable is 2.00 rad/s. A ball of clay, with a mass of 40.0 g, is dropped from a height of 35.0 cm above the turntable. It hits the turntable at a distance of 15.0 cm from the middle, and sticks...
A disk of mass m radius R, and area A has a su tace mass de sity Ơ(r - where r is the distance rrom the center or the disk to a specific point on the disk see the follo ino rigure what is the moment or inertia or the disk about an axis through the center? Use AR the following as necessary: m and R.) Axis of rotation
A disk of mass m radius R, and area A has...