Question

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 the rod. When the bug has reached the end of the rod and sits there, its tangential speed is 0.108 m/s . The bug can be treated as a point mass. Part A: what is the mass of the rod? Correct answer 5.19 x 10^-2 kg Part B: what is the mass of the bug?

Answer #1

a) Moment of inertia of a rod about an endpoint

I = 1/3 * m * L^2

m = 3 * I / L^2

m = 3 * 3.20 * 10^(-3) / 0.430^2

mass of rod m = 0.0519 kg = 5.19*10^(-2) kg

b) The angular momentum L is conserved:

The new angular velocity is

w = v/R = 0.108 m/s / 0.43 m = 0.251 rad/s

L1 = I * w1 = 3.20 * 10^(-3) * 0.32

L2 = I * w2 + I(bug) * w2

= 3.20 * 10^(-3) * 0.251 + m(bug) * 0.43^2 * 0.251

I(bug) = mL^2

L1 = L2

3.20 * 10^(-3) * 0.32 = 3.20 * 10^(-3) * 0.251 + m(bug) * 0.43^2 * 0.251

m(bug) = ( 3.20 * 10^(-3) * 0.32 - 3.20 * 10^(-3) * 0.251) / (0.43^2 * 0.251)

m(bug) = 4.757 * 10^(-3) kg

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 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 rod has a length of 0.380 m and rotates in a circle on a
frictionless tabletop. The axis is perpendicular to the length of
the rod at one of its ends. The rod has an angular velocity of
0.428 rad/s and a moment of inertia of 1.31 x 10 −3 kg·m 2 . A bug
standing on the axis decides to crawl out to the other end of the
rod. When the bug (whose mass is 5.00 x...

A thin rod has a length of 0.380 m and rotates in a circle on a
frictionless tabletop. The axis is perpendicular to the length of
the rod at one of its ends. The rod has an angular velocity of
0.428 rad/s and a moment of inertia of 1.31 x 10 −3 kg·m 2 . A bug
standing on the axis decides to crawl out to the other end of the
rod. When the bug (whose mass is 5.00 x...

Interactive Solution 9.63 illustrates one way of solving a
problem similar to this one. A thin rod has a length of 0.594 m and
rotates in a circle on a frictionless tabletop. The axis is
perpendicular to the length of the rod at one of its ends. The rod
has an angular velocity of 0.673 rad/s and a moment of inertia of
1.37 x 10-3 kg·m2. A bug standing on the axis decides to crawl out
to the other end...

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

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 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 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...

1) A torque of 1.20 N m is applied to a thin rod of mass 2.50 kg
and length 50.0 cm pivoted about its center and at rest. How fast
is the rod spinning after 4.25 s?
a. 32.6 rad/s
b. 8.16 rad/s
c. 97.9 rad/s
d. 24.5 rad/s
2) A torque of 1.20 N m is applied to a thin rod of mass 2.50 kg
and length 50.0 cm pivoted about one end and at rest. How fast is...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 24 minutes ago

asked 24 minutes ago

asked 45 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 1 hour ago

asked 1 hour ago

asked 2 hours ago