Question

A cylindrical rod of length 2.0 m, radius 0.5 m, and mass 1.5 kg
has two spheres attached on its ends. The centers of the spheres
are 1.0 m from the center of the rod. The mass of each sphere is
0.66 kg. The rod is capable of rotating about an axis passing
through its center and perpendicular to the plane of the page, but
the set up is stationary to begin with. A small mass of value 0.19
kgmoving with a velocity * v* = 2.5 m/s strikes the
bottom mass of the dumbbell and sticks to it. At the same instant,
a second mass of equal value but moving with twice the velocity
strikes the top mass of the dumbbell and sticks to it. The entire
system starts to rotate. Determine the magnitude and direction of
the angular velocity of the system after the collision. Treat the
two moving masses and the masses at the end of the rod like point
particles.

Magnitude:

Direction:

Answer #1

A cylindrical rod of mass 0.82 kg and length 1.88 m is free to
rotate about a pivot fixed at one end. A ball with a mass of 3.2 kg
is attached to the other end of the rod. The rod-and ball system is
held in a horizontal position by a vertical force that acts 1.41 m
from the pivot. The force is then removed, and the rod-and-ball
swings down.
(a) What was the vertical force used to hold the...

A cylindrical rod of mass 0.82 kg and length 1.88 m is free to
rotate about a pivot fixed at one end. A ball (mass 3.2 kg) is
attached to the other end of the rod. The rod-and- ball system is
held in a horizontal position by a vertical force that acts 1.41 m
from the pivot. The force is then removed, and the rod-and-ball
swings down.
(a) (4 points) What was the vertical force used to hold the
system...

The uniform thin rod in the figure below has mass M =
2.00 kg and length L = 2.87 m and is free to rotate on a
frictionless pin. At the instant the rod is released from rest in
the horizontal position, find the magnitude of the rod's angular
acceleration, the tangential acceleration of the rod's center of
mass, and the tangential acceleration of the rod's free end.
HINT
An illustration shows the horizontal initial position and
vertical final position...

A uniform thin rod of length 0.45 m and mass 6.5 kg can rotate
in a horizontal plane about a vertical axis through its center. The
rod is a rest when a 3.0-g bullet traveling in the horizontal plane
of the rod is fired into one end of the rod. As viewed from above,
the direction of the bullet velocity makes an angle of 60° with the
rod (see the figure). If the bullet lodges in the rod and the...

A uniform rod of mass 3.40×10−2 kg and length 0.410 m
rotates in a horizontal plane about a fixed axis through its center
and perpendicular to the rod. Two small rings, each with mass 0.190
kg , are mounted so that they can slide along the rod. They are
initially held by catches at positions a distance
5.50×10−2 m on each side from the center of the rod, and
the system is rotating at an angular velocity 28.0 rev/min ....

A rod of length l=1.1m and mass M= 5.5kg joins two particles
with masses m1 =4.8kg and m2 = 2.8kg, at its ends. The combination
rotates in the xy-plane about a pivot through the center of the rod
with the linear speed of the masses of v= 3.5 m/s. (Moment of
inertia of a uniform rod rotating about its center of mass I= 1 12
M l2 ) angularmomentum a) Calculate the total moment of inertia of
the system I...

A rod of length l=2.2m and mass M= 9.7kg joins two particles
with masses m1 =12.9kg and m2 = 5.0kg, at its
ends. The combination rotates in the xy-plane about a pivot through
the center of the rod with the linear speed of the masses of v=
12.9 m/s. (Moment of inertia of a uniform rod rotating about its
center of mass
I=
1
12
M l2
)
a) Calculate the total moment of inertia of the system
I =...

(a)
A light, rigid rod of length
ℓ = 1.00 m
joins two particles, with masses
m1 = 4.00 kg
and
m2 = 3.00 kg,
at its ends. The combination rotates in the xy-plane
about a pivot through the center of the rod (see figure below).
Determine the angular momentum of the system about the origin when
the speed of each particle is 4.80 m/s. (Enter the magnitude to at
least two decimal places in kg · m2/s.)
Two masses...

a rod 2.5 m long with mass 10 kg can rotate freely about a
horizontal axis through the end of the rod.
a bullet with mass 15 grams or 0.015 kg with a speed of 400 m/s
strikes center of the rod in a direction perpendicular to the rod,
and is embedded there.
What is the rod's angular speed after the bullet stops in the
rod?

A point object with mass 6 kg and a uniform rigid rod with mass
6 kg and length 11 meter are on a horizontal
frictionless planar surface. Point object hits the rod vertically
with velocity 8 m/s and sticks to the rod.
Part A
Calculate the angular velocity ω about the center of mass just
after the point object with mass m sticks to the rod.
Part B
Calculate the ratio of the lost energy to the initial kinetic
energy of...

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