Question

A cylindrical rod of uniform density is located with its center
at the origin, and its axis along the *x* axis. It rotates
about its center in the *xy* plane, making one revolution
every 0.07 s. The rod has a radius of 0.06 m, length of 0.5 m, and
mass of 7 kg. What is the rotational kinetic energy of the rod?

Answer #1

A lawn mower has a flat, rod-shaped steel blade that rotates
about its center. The mass of the blade is 0.65 kg and its length
is 0.55 m
What is the rotational energy of the blade at its operating
angular speed of 3490 rpm ?
If all of the rotational kinetic energy of the blade could be
converted to gravitational potential energy, to what height would
the blade rise?

A propeller is modeled as five identical uniform rods extending
radially from its axis. The length and mass of each rod are 0.803 m
and 2.61 kg, respectively. When the propellor rotates at 577 rpm
(revolutions per minute), what is its rotational kinetic
energy?

A propeller is modeled as five identical uniform rods extending
radially from its axis. The length and mass of each rod are 0.781
m0.781 m and 2.85 kg2.85 kg, respectively. When the propellor
rotates at 597 rpm597 rpm (revolutions per minute), what is its
rotational kinetic energy K?

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.

A rod of length l=0.8m and mass M= 3.7kg joins two particles
with masses m1 =4.5kg 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
a) Calculate the total moment of inertia of the system
b) What is...

A uniform, 0.0350 kg rod of length 0.450 m rotates in a
horizontal plane about a fixed axis through its center and
perpendicular to the rod. Two small rings, each with mass 0.0200
kg, are mounted so that they can slide without friction along the
rod. They are initially held by catches at positions 0.0550 m on
each side of the center of the rod, and the system is rotating at
48.0 rev/min. With no other changes in the system,...

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 charge of uniform linear density 2.12 nC/m is distributed
along a long, thin, nonconducting rod. The rod is coaxial with a
long conducting cylindrical shell with an inner radius of 6.47 cm
and an outer radius of 12.0 cm. If the net charge on the shell is
zero,
a) what is the surface charge density on the inner surface of
the shell?
b) What is the surface charge density on the outer surface of
the shell?

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 =...

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