Question

The following four objects (each of mass m) roll without slipping down a ramp of height h:

Object 1: solid cylinder of radius r

Object 2: solid cylinder of radius 2r

Object 3: hoop of radius r

Object 4: solid sphere of radius 2r

Rank these four objects on the basis of their rotational kinetic energy at the bottom of the ramp.

Answer #1

Four objects with the same mass and radius roll without slipping
down an incline. If they all start at the same location, which
object will take the longest time to reach the bottom of the
incline? Mass Moment of Inertia Table Choices A. A hollow sphere B.
A solid sphere C. A thin-wall hollow cylinder D. They all take the
same time E. A solid cylinder

Four objects—a hoop, a solid cylinder, a solid sphere, and a
thin, spherical shell—each have a mass of 4.06 kg and a radius of
0.253 m.
(a) Find the moment of inertia for each object as it rotates
about the axes shown in this table.
hoop
___ kg · m2
solid cylinder
___ kg · m2
solid sphere
___ kg · m2
thin, spherical shell
___ kg · m2
(b) Suppose each object is rolled down a ramp. Rank the...

Two objects of equal mass m are at rest at the top of a hill of
height h. Object 1 is a circular hoop of radius r, and object 2 is
a solid disc, also of radius r. The object are released from rest
and roll without slipping.
A) Provide expressions for the LINEAR VELOCITY of each object
once it reaches the bottom of the hill. Careful - you should
provide two answers!
B) Considering your results from part A,...

A 1.6 m radius cylinder with a mass of 8.6 kg rolls without
slipping down a hill which is 5.6 meters high. At the bottom of the
hill, what percentage of its total kinetic energy is invested in
rotational kinetic energy?

Consider the following three objects, each of the same mass and
radius:
1) Solid Sphere
2) Solid Disk
3) Hoop.
All three are release from rest at top of an inclined plane. The
three objects proceed down the incline undergoing rolling motion
without slipping. use work-kinetic energy theorem to determine
which object will reach the bottom of the incline first

A ball rolls down a ramp without slipping. It starts from
rest.
(a) Specify the mass and radius of the ball, and the height and
length of the ramp.
(b) Calculate the moment of inertia of the ball
. (c) Calculate the potential energy of the ball at the top of
the ramp.
(d) Calculate the linear kinetic energy and rotational kinetic
energy of the ball.
(e) Determine the angular acceleration of the ball.
(f) Determine how long the ball...

Two objects roll down a hill: a hoop and a solid cylinder. The
hill has an elevation change of 1.4-m and each object has the same
diameter (0.55-m) and mass. Calculate the velocity of each object
at the bottom of the hill and rank them according to their
speeds.
[Hint: When an object is rolling, the
angular speed and the velocity of the center of mass are related by
, where is the radius of the object.]
Veyi= 4.3 m/s...

1. A solid sphere of mass 50 kg rolls without slipping. If the
center-of-mass of the sphere has a translational speed of 4.0 m/s,
the total kinetic energy of the sphere is
2.
A solid sphere (I = 0.4MR2) of
radius 0.0600 m and mass 0.500 kg rolls without slipping down an
inclined plane of height 1.60 m . At the bottom of the plane, the
linear velocity of the center of mass of the sphere is
approximately
_______ m/s.

Consider the objects below, all of mass M and radius R (where
appropriate). They are placed on an incline plane at the same
height. Which object will roll down the incline and reach the
bottom with the greatest total energy?
a) A solid sphere
b) A thin spherical shell
c) A solid cylinder of length L
d) A cylindrical shell of length L
e) All will reach bottom with same energy
Group of answer choices
A solid sphere
A thin...

Problem 4
A hoop and a solid disk both with Mass (M=0.5 kg) and radius (R=
0.5 m) are placed at the top of an incline at height (h= 10.0 m).
The objects are released from rest and rolls down without
slipping.
a) The solid disk reaches to the bottom of the inclined plane
before the hoop. explain why?
b) Calculate the rotational inertia (moment of inertia) for the
hoop.
c) Calculate the rotational inertia (moment of inertia) for the...

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