Question

A solid, homogeneous sphere with of mass of M = 2.25 kg and a radius of R = 11.3 cm is resting at the top of an incline as shown in the figure. The height of the incline is h = 1.65 m, and the angle of the incline is θ = 17.3°. The sphere is rolled over the edge very slowly. Then it rolls down to the bottom of the incline without slipping. What is the final speed of the sphere?

Answer #1

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...

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.

An 8 kg solid sphere has a radius of 70 mm and anangular
velocity of 60 rpm at the top of a 30 degree incline. At the bottom
of the incline it has an angular velocity of 15x60 rpm. Assume the
sphere rolls without slipping. Find the height of the incline in
meters.
The answer is 3.092 m. How do I get there?

In the figure, a solid cylinder of radius 5.3 cm and mass 17 kg
starts from rest and rolls without slipping a distance L = 7.6 m
down a roof that is inclined at angle θ = 22°. (a) What is the
angular speed of the cylinder about its center as it leaves the
roof? (b) The roof's edge is at height H = 3.8 m. How far
horizontally from the roof's edge does the cylinder hit the level
ground?

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.

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 solid sphere of mass 0.6010 kg rolls without slipping along a
horizontal surface with a translational speed of 5.420 m/s. It
comes to an incline that makes an angle of 31.00° with the
horizontal surface. To what vertical height above the horizontal
surface does the sphere rise on the incline?

An 6.90-cm-diameter, 360 g solid sphere is released from rest at
the top of a 1.80-m-long, 20.0 ∘ incline. It rolls, without
slipping, to the bottom. What is the sphere's angular velocity at
the bottom of the incline? What fraction of its kinetic energy is
rotational?

A solid sphere with a moment of inertia of I = 2/5 M R2 is
rolled down an incline which is inclined at 24 degrees. The radius
of the sphere is 1.6 meters. The initial velocity of the center of
mass at the top of the incline is 2 m/s. As the sphere rolls
without slipping down the incline, it makes 26 revolutions as it
travels all the way down the incline. How long, in seconds, does it
take to...

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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