Question

Consider a rod that is 0.220 cm in diameter and 1.50 m long, with a mass of 0.0400 kg.

1. Find the moment of inertia about an axis perpendicular to the rod and passing through one end.(kg*m^2 units please)

2. Find the moment of inertia about an axis along the length of the rod.

Express your answer in kilogram meters squared.

Answer #1

Solution:

Given:

Diameter (d) = 0.22 cm = 2.2 x 10^{-3} m

Thus : r = 1.1 x 10^{-3} m

Length (L) = 1.50 m

Mass (m) = 0.04 kg

the moment of inertia about an axis perpendicular to the rod and
passing through its center = I_{C} = (1/2)
ML^{2}

^{Thus :} I_{c} = (0.5)(0.04)(1.50)^{2}
= 0.045 kg m^{2}

Now : using parallel axis theorem :

the moment of inertia about an axis perpendicular to the rod and
passing through one end (I_{end}) = I_{C} + m
d^{2}

I_{end} = (0.045) + M (L/2)^{2}

I_{end} = (0.045) + (0.04) (1.50/2)^{2}

**I _{end} = 0.0675 kg m^{2}**

the moment of inertia about an axis along the length of the rod
= (1/2) m r^{2} = (0.5)(0.04)(1.1 x 10^{-3}
m)^{2} = **2.42 x 10 ^{-8} kg
m^{2}**

Find the moment of inertia about each of the following axes for
a rod that has a diameter of d, a length of l, and a mass of m. A)
About an axis perpendicular to the rod and passing through its
center. B) About an axis perpendicular to the rod and passing
through one end. C) About a longitudinal axis passing through the
center of the rod.

A 1.50-kg rod 1.00m long has a 2.00-kg mass attached to one end
and a 4.00-kg mass attached to the other. The system rotates at a
constant angular speed about a fixed axis perpendicular to the rod
that passes through the rod 40.0 cm from the end with the 4.00-kg
mass attached. The angular speed of the system is 150 rad/s.
a) What is the total moment of inertia of this system (including
the rod and two masses) about the...

Uniform rod with length 6.6 m and mass 9.2 kg is rotating about
an axis passing distance 4 m from one of its ends. The moment of
inertia of the rod about this axis (in kg m2) is

) A dumbbell-shaped object is composed by two equal masses, m,
connected by a rod of negligible mass and length r. If I1 is the
moment of inertia of this object with respect to an axis passing
through the center of the rod and perpendicular to it and I2 is the
moment of inertia with respect to an axis passing through one of
the masses and perpendicular to the rod, it follows that
a. It depends on the values of...

A thin, rigid, uniform rod has a mass of 1.40 kg and a length of
2.50 m. (a) Find the moment of inertia of the rod relative to an
axis that is perpendicular to the rod at one end. (b) Suppose all
the mass of the rod were located at a single point. Determine the
perpendicular distance of this point from the axis in part (a),
such that this point particle has the same moment of inertia as the
rod...

A long, uniform rod of length 0.510 mm 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 0.4 rad/srad/s and a
moment of inertia about the axis of 2.70×10−3 kg⋅m2kg⋅m2
. An insect initially standing on the rod at the axis of rotation
decides to walk to the other end of the rod. When the...

A thin, uniform rod is bent into a square of side length a. If
the total mass of the rod is M, find the moment of inertia about an
axis through the center and perpendicular to the plane formed by
the interior of the square.
Thanks!

A rod 2 m long, 2 cm in diameter and 5 kg in mass is fixed at
one end and is stricken by a force F to produce a 3rd overtone and
elongates at 1 cm. A string of length L and mass 750 grams is puled
by a T = 30 to produce a 3rd harmonic frequency. Determine the
force F and length L that produces the same value of frequencies in
the two materials, if the sound wave...

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 0.400 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 0.34 rad/s and a
moment of inertia about the axis of 2.50×10−3 kg⋅m2 . A bug
initially standing on the rod at the axis of rotation decides to
crawl out to the other end of...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 9 minutes ago

asked 12 minutes ago

asked 12 minutes ago

asked 27 minutes ago

asked 27 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago