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4. (Extra Credit) In this problem you will derive the formula for the rotational inertia of...
Results given on page 300: TABLE 12.2 Moments of inertia of objects with uniform density Object...
Results given on page 300: TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod about center Cylinder or disk, ML MR2 about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Solid sphere, about diameter 3MR2 Plane or slab, about edge Ma Spherical shell, about diameter MR2 4. Use the results on page 300 of the textbook to do the following: A...
4. Use the results on page 300 of the textbook to do the following: solid, uniform...
4. Use the results on page 300 of the textbook to do the following: solid, uniform disk has a mass of 35.0 kg and outer radius 40.0 cm. Attached to the disk at a point 270 cm from the disk's center is a heavy metal bolt of mass 1.00 kg. By what percentage does the bolt increase the overall moment of inertia around an axis through the disk's center (and perpendicular to the plane of the disk)? Treat the bolt...
This is the diagram that was provided. 3. It can be shown that the rotational inertia (moment of inertia) for a uniform...
This is the diagram that was provided.
3. It can be shown that the rotational inertia (moment of inertia) for a uniform rod about an axis that's perpendicular to the rod and passes through one of its ends is: Where M is the rod's total mass and L is its total length. (a) (10 points) Use the Parallel Axis Theorem to find the moment of inertia of a uniform rod about an axis that's perpendicular to the rod and passes...
Q1. See the course content for a short review of moment of inertia where you will...
Q1. See the course content for a short review of moment of inertia where you will also find a problem solving video on this topic. . Find the moment of inertia of a uniform thin rod with mass M and length L rotating about its center (a thin rod is a 1D object; in the figure the rod has a thickness for clarity): For this problem, use a coordinate axis with its origin at the rod's center and let the...
Page 2 Rotational Motion Questions The formula for the moment of inertia of our disk rotating...
Page 2 Rotational Motion Questions The formula for the moment of inertia of our disk rotating about its center is I-(1/2)MR2. Calculate the moment of inertia for the three following combinations of 1. mass and radii: ) IfRi 0.150 m and M 4.450kg, then I =? ii) If R2 0.050 m and M2 20.000kg, then I =? iii) If Ry 2.500 m and M3 0.0080kg, then I3 = ? iv) In determining the moment of inertia of an object with...
4. b. Refer to the drawing here. A solid, uniform disk has a mass of M...
4. b. Refer to the drawing here. A solid, uniform disk has a mass of M and outer radius R A heavy metal bolt of mass m is attached to the disk at a point that is located a distance r from the disk's center. (overhead view) R: The bolt and the disk center lie along one diameter across the disk. Consider a second diameter that is perpendicular to the one containing the bolt; and let point P be located...
6. A disk with a mass M, a radius R, and a rotational inertia of I-...
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
A non-uniform density cylinder has a radius R=6m. The rotational inertia of this cylinder can be...
A non-uniform density cylinder has a radius R=6m. The rotational inertia of this cylinder can be taken to be I=βMR2, where β is unknown and M is the mass of the cylinder. The cylinder is initially rotating with angular velocity ω0= 1.00rad/s, and is placed on a rough horizontal surface. The speed of the center of mass (CM) of the cylinder, as it is placed on the surface, is 0. The cylinder at first rolls and slips. Just as it...
Derive the formula for the moment of inertia of a uniform, flat, rectangular plate of dimensions&x...
Derive the formula for the moment of inertia of a uniform, flat, rectangular plate of dimensions&x w about an axis through its center, perpendicular to the plate. Express your answer in terms of the variables 1, w, and M. Xi Submit My Answers Give Up Incorrect; Try Again; 14 attempts remaining Part B What is the moment of inertia about each of the axes through the center that are parallel to the edges of the plate? Express your answers in...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere behe.A massless cord passes around the equator of the sphere, overs pulley with rotational inertial and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. Att 0, the mass m has speed Vo The system is...
Results given on page 300: TABLE 12.2 Moments of inertia of objects with uniform density Object and axis Picture Object and axis Picture Thin rod about center Cylinder or disk, ML MR2 about center Thin rod about end ML Cylindrical hoop, MR2 about center Plane or slab, about center Solid sphere, about diameter 3MR2 Plane or slab, about edge Ma Spherical shell, about diameter MR2 4. Use the results on page 300 of the textbook to do the following: A...
4. Use the results on page 300 of the textbook to do the following: solid, uniform disk has a mass of 35.0 kg and outer radius 40.0 cm. Attached to the disk at a point 270 cm from the disk's center is a heavy metal bolt of mass 1.00 kg. By what percentage does the bolt increase the overall moment of inertia around an axis through the disk's center (and perpendicular to the plane of the disk)? Treat the bolt...
This is the diagram that was provided.
3. It can be shown that the rotational inertia (moment of inertia) for a uniform rod about an axis that's perpendicular to the rod and passes through one of its ends is: Where M is the rod's total mass and L is its total length. (a) (10 points) Use the Parallel Axis Theorem to find the moment of inertia of a uniform rod about an axis that's perpendicular to the rod and passes...
Q1. See the course content for a short review of moment of inertia where you will also find a problem solving video on this topic. . Find the moment of inertia of a uniform thin rod with mass M and length L rotating about its center (a thin rod is a 1D object; in the figure the rod has a thickness for clarity): For this problem, use a coordinate axis with its origin at the rod's center and let the...
Page 2 Rotational Motion Questions The formula for the moment of inertia of our disk rotating about its center is I-(1/2)MR2. Calculate the moment of inertia for the three following combinations of 1. mass and radii: ) IfRi 0.150 m and M 4.450kg, then I =? ii) If R2 0.050 m and M2 20.000kg, then I =? iii) If Ry 2.500 m and M3 0.0080kg, then I3 = ? iv) In determining the moment of inertia of an object with...
4. b. Refer to the drawing here. A solid, uniform disk has a mass of M and outer radius R A heavy metal bolt of mass m is attached to the disk at a point that is located a distance r from the disk's center. (overhead view) R: The bolt and the disk center lie along one diameter across the disk. Consider a second diameter that is perpendicular to the one containing the bolt; and let point P be located...
6. A disk with a mass M, a radius R, and a rotational inertia of I- MR is attached to a horizontal spring which has a spring constant of as shown in the diagram. When the spring is stretched by a distance x and then released from rest, the disk rolls without slipping while the spring is attached to the frictionless axle within the center of the disk (a) Calculate the maximum translational velocity of the disk in terms of...
Derive the formula for the moment of inertia of a uniform, flat, rectangular plate of dimensions&x w about an axis through its center, perpendicular to the plate. Express your answer in terms of the variables 1, w, and M. Xi Submit My Answers Give Up Incorrect; Try Again; 14 attempts remaining Part B What is the moment of inertia about each of the axes through the center that are parallel to the edges of the plate? Express your answers in...
A sphere of radius R can rotate about a vertical axis on frictionless bearings (see figure below). Let the rotational inertia of the sphere behe.A massless cord passes around the equator of the sphere, overs pulley with rotational inertial and radius r, and is attached to a small object of mass m. There is no friction on the pulley's axle and the cord does not slip on the pulley. Att 0, the mass m has speed Vo The system is...
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