Question

A thin uniform rod with mass m swings about an axis that passes through one end of the rod and is perpendicular to the plane of the swing. The rod swings with a period T and an angular amplitude of φm (assume this angle is sufficiently small to allow for the use of the equations in this chapter). (a) What is the length of the rod? (b) What is the maximum kinetic energy of the rod as it swings? State your answers in terms of the given variables, using g and π when applicable. (a)L = (b)Km =

Answer #1

A uniform thin rod of length 0.56 m and mass 3.2 kg can rotate
in a horizontal plane about a vertical axis through its center. The
rod is at rest when a 3.5 g bullet traveling in the rotation plane
is fired into one end of the rod. As viewed from above, the
bullet's path makes angle θ = 60° with the rod. If the
bullet lodges in the rod and the angular velocity of the rod is
12.0 rad/s...

A uniform rod of length L and mass M is free to swing about an
axis that is perpendicular to the rod. The axis is a distance x
from the rod's center of mass.
a) Find the period of oscillations for small angles as a
function of L and x with appropriate constants.
b) make a sketch of the period as a function of x. If you use a
spread sheet you may assume that L=1.0 m, then your graph...

A thin uniform rod has a length of 0.490 m and is rotating in a
circle on a frictionless table. The axis of rotation is
perpendicular to the length of the rod at one end and is
stationary. The rod has an angular velocity of 0.37 rad/s and a
moment of inertia about the axis of 3.50×10−3 kg⋅m2 . A
bug initially standing on the rod at the axis of rotation decides
to crawl out to the other end of...

A uniform thin rod of length 0.766 m is hung from a horizontal
nail passing through a small hole in the rod located 0.044 m from
the rod's end. When the rod is set swinging about the nail at small
amplitude, what is the period T of oscillation? T=______ s

An object is formed by attaching a uniform, thin rod with a mass
of mr = 7.22 kg and length L = 5.52 m to a uniform
sphere with mass ms = 36.1 kg and radius R = 1.38 m.
Note ms = 5mr and L = 4R.
1)What is the moment of inertia of the object about an axis at
the left end of the rod?
2)If the object is fixed at the left end of the rod, what...

A thin uniform rod has a length of 0.430 m and is rotating in a
circle on a frictionless table. The axis of rotation is
perpendicular to the length of the rod at one end and is
stationary. The rod has an angular velocity of 0.32 rad/s and a
moment of inertia about the axis of 3.20×10−3 kg⋅m2 . A bug
initially standing on the rod at the axis of rotation decides to
crawl out to the other end of...

A uniform rod of mass M and length L is pivoted at one
end. The rod is left to freely rotate under the influence of its
own weight. Find its angular acceleration α when it makes
an angle 30° with the vertical axis. Solve for M=1 Kg, L=1 m,
take g=10 m s-2. Hint: Find the center of mass for the rod, and
calculate the torque, then apply Newton as τ= Ι·α

A uniform rod of mass M and length L is pivoted at one end. The
rod is left to freely rotate under the influence of its own weight.
Find its angular acceleration α when it makes an angle 30° with the
vertical axis. Solve for M=1 Kg, L=1 m, take g=10 m s-2. Your
answer in X.X rad s-2. Hint: Find the center of mass for the rod,
and calculate the torque, then apply Newton as τ= Ι·α

A uniform rod of mass 250 g and length 75 cm
is free to rotate in a horizontal plane around a fixed vertical
axis through its center, perpendicular to its length. Two small
beads, each of mass 25 g, are mounted in grooves along the
rod. Initially, the two beads are held by catches on opposite sides
of the rod’s center, 9 cm from the axis of rotation. With
the beads in this position, the rod is rotating with an...

A thin, 1-dimensional, uniform rod of mass M and length L lies
on the x axis with one end at the origin.
(a) Find its moment of inertia tensor about the origin.
(b) Find the moment of inertia tensor if the rod’s center is
located at the origin.

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