Question

**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 solid disk.

d)Calculate the potential energy of both object before they were released from

the top the incline.

e)Use conservation of energy to find the velocity of the hoop at the bottom the incline.

f) Use conservation of energy to find the velocity of the solid desk at the bottom the incline.

g) which one has more velocity? Does your answers (for e and f) prove your response to part a. ?

Answer #1

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An object (either solid sphere, hoop or solid disk) of Mass
M=10kg and radius R=4m is at the
bottom of an incline having inclination angle X=40 degrees
and base length X=15 meters, with an initial rotational
velocity omega(i)=2rad/s; it is subsequently
pulled up the the incline by some force F=15
(Newtons) such that at the top of the incline it
has a final rotational velocity omega(f)=7rad/s.
Determine: a) the linear velocity, b) rotational KE and c) total
work and work...

A hoop and a disk, both of 0.88- m radius and 4.0- kg mass, are
released from the top of an inclined plane 3.3 m high and 8.1 m
long. What is the speed of each when it reaches the bottom? Assume
that they both roll without slipping. What is the speed of the
hoop? What is the speed of the disk?

A hoop and a disk, both of 0.50- m radius and 4.0- kg mass, are
released from the top of an inclined plane 2.9 m high and 8.7 m
long. What is the speed of each when it reaches the bottom? Assume
that they both roll without slipping. What is the speed of the
hoop? What is the speed of the disk?

A hollow cylinder (hoop) of mass M and radius R starts rolling
without slipping (with negligible initial speed) from the top of an
inclined plane with angle theta. The cylinder is initially at a
height h from the bottom of the inclined plane. The coefficient of
friction is u. The moment of inertia of the hoop for the rolling
motion described is I= mR^2.
a) What is the magnitude of the net force and net torque acting
on the hoop?...

A thin hoop and a solid disk having the same mass and outer
radii of 1.3 g and 43 mm, respectively, are released from rest as
shown. Each rolls without slipping. D28Determine the kinetic energy
in J and the angular velocity in radian/s of each having travelled
a distance of 2.1 m down the 6 deg incline: (a) thin hoop and (b)
solid cylilnder.

A sphere of mass M, radius r, and rotational inertia I is
released from rest at the top of an inclined plane of height h as
shown above. (diagram not shown)
If the plane has friction so that the sphere rolls without
slipping, what is the speed vcm of the center of mass at the bottom
of the incline?

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 uniform disc of mass M=2.0 kg and radius R=0.45 m rolls
without slipping down an inclined plane of length L=40 m and slope
of 30°. The disk starts from rest at the top of the incline. Find
the angular velocity at the bottom of the incline.

QUESTION 27
A uniform disk of radius 0.40 m and mass 31.0 kg rolls on a
plane without slipping with angular speed 3.0 rad/s. The rotational
kinetic energy of the disk is __________. The moment of inertia of
the disk is given by 0.5MR2.

A disk with a c value of 1/2, a mass of 9 kg, and radius of 0.26
meters, rolls without slipping down an incline with has a length of
9 meters and angle of 30 degrees. At the top of the incline the
disk is spinning at 37 rad/s. What is the rotational kinetic energy
of the disk at the bottom of the incline in Joules?

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