rotation of uniform cylinder about a horizontal axis

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A uniform cylinder of radius 10 cm and mass 20 kg is mounted so as to rotate freely about a horizontal axis that is parallel to and 5.0 cm form the central longitudinal axis of the cylinder. a) What is the rotational inertia of the cylinder about the axis of rotation? b) If the cylinder is released from rest with its central longitudinal axis at the same height as the axis about which the cylinder rotates, what is the angular speed of the cylinder as it passes through its lowest position?

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Please see the attached file for detailed solution.

(a) First, draw a picture of this system. (a) shows an end-on view of the rotating cylinder. Its symmetry axis is labeled "CM" but its rotational axis is marked "Axis".
The cylinder does not ...

Solution Summary

The solution is comprised of detailed explanation of the rotation of a uniform cylinder about a horizontal axis, which is parallel to the central longitudinal axis of the cylinder. The rotational inertia and the angular speed of the cylinder are calculated with step-by-step explanations and graphs.

Solid, uniformcylinder of mass m and radius R is fitted with a frictionless axle along the cylinder's long axis. A horizontal spring (spring constant k) is attached to this axle. Under the influence of the spring, the cylinder rolls back and forth without slipping on a horizontal surface. What is the frequency of this motion?

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A sphere and cylinder are released from rest on the ramp at t = 0. If each has a mass m and A radius r, determine their angular velocities at time t. Assume no slipping occurs.
See attached file for full problem description.

A uniformcylinder, mass M= 12 kg, radius R= .36 m, is initially rotating about a vertical axis through its center at angular velocity wo= 6.6 rad/sec. Now two small (point masses), each of mass m= 2 kg, are dropped onto and stick to the cylinder, each at distance r= .24 m from the axis. SEE ATTACHMENT for diagram.
Find wf, t

A timber of uniform cross section with a mass of 90 kg is hinged at its lower end and held at angle of 60 degrees with the horizontal by a rod attached as shown in (attached figure 4-6)
A cylinder which has a mass of 30 kg is placed between the timber and the wall.
1) What are the horizontal and vertical components of the r

A solid cylinder of mass 8kg and diameter 20cm is rotated about an axis parallel to its central axis at a distance of 10 cm from the cylinder. the rotatinal inertia of the cylinderabout the parallel axis is:
a. 0.12 kg m^2
b. 0.08 kg m^2
c. 12 kg m^2
d. 0.04 kg m^2

Moment of inertia problem
A uniformcylinder has mass M and radius R.
a. Find by integration the moment of inertia, Io, about its center of mass
axis at center, perpendicular to the face of the cylinder.
b. Use the translation of axis theorem, 'Ip = Io + M h^2' to find the moment of inertia about an axis parallel to that

Please see the attached file:
3. Consider the case of an infinite conducting cylinder of radius 'a' with a uniform charge per unit length lambda placed in a uniform electric field with the axis of the cylinder perpendicular to the direction of the field. The potential generated by such a system maybe written as: (See attachme

A uniform hollow cylinder such as a roll of paper towels, has mass M, inner radius Ri, outer radius Ro. By applying 'I= Int (r^2 dm)', find its moment of inertia about a center of mass axis along its diameter.
See attachment for diagram.