Question

**A disc, which has a mass of 12.0 kg and a radius of 65.0
cm., sits at the top of an inclined plane, which is 8.40 meters
long and 1.50 meters high. At t = 0 the disc is released and is
allowed to roll to the bottom of the incline without
slipping.**

**a. What is the GPE of this disc as it sits at the top of
the incline?**

**b. What will be the total kinetic energy of this disc as
it reaches the bottom of the incline?**

**c. What will be the linear velocity of this disc when it
reaches the bottom of the inclined plane?**

**d. What would the linear velocity be if the disc is
replaced by a sphere?**

**e. What would the velocity be if the object was a
ring?**

Answer #1

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.

A
2.9 kg solid sphere (radius = 0.15 m) is released from rest at the
top of a ramp and allowed to roll without slipping. The ramp is
0.85 m high and 5.2 m long.
1. When the sphere reaches the bottom of the ramp, what are
its total kinetic energy,
2. When the sphere reaches the bottom of the ramp, what is its
rotational kinetic energy?
3. When the sphere reaches the bottom of the ramp, what is its...

A block with a mass of 12.0 kg is initially at rest at the top
of a plane that is inclined at an angle of 30.0° above the
horizontal. The block slides down the plane and is traveling with a
speed of 1.50 m/s when it reaches the bottom. If the plane is 0.750
m long, what is the coefficient of kinetic friction between the
block and the plane? please explain each step.

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?

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 uniform, solid sphere of radius 3.00 cm and mass 2.00 kg
starts with a purely translational speed of 1.25 m/s at the top of
an inclined plane. The surface of the incline is 1.00 m long, and
is tilted at an angle of 25.0 ∘ with respect to the horizontal.
Assuming the sphere rolls without slipping down the incline,
calculate the sphere's final translational speed v 2 at the bottom
of the ramp.

A uniform, solid sphere of radius 5.75 cm 5.75 cm and mass 3.25
kg 3.25 kg starts with a purely translational speed of 1.25 m/s
1.25 m/s at the top of an inclined plane. The surface of the
incline is 2.25 m 2.25 m long, and is tilted at an angle of 29.0 ∘
29.0∘ with respect to the horizontal. Assuming the sphere rolls
without slipping down the incline, calculate the sphere's final
translational speed ? 2 v2 at the...

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...

A cylindrical ring of mass 0.920 kg and radius of 7.62 cm is
rolling down an inclined plane without slipping. If rotational
energy at the bottom is 7.36 J what is the translation velocity

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