Question

In the figure, a solid cylinder of radius 24 cm and mass 16 kg
starts from rest and rolls without slipping a distance *L* =
7.9 m down a roof that is inclined at angle *θ* = 38°.
**(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* = 4.3 m. How far horizontally
from the roof's edge does the cylinder hit the level ground?

Answer #1

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?

In the figure below, a solid cylinder of radius 14 cm and mass
17 kg starts from rest and rolls without slipping a distance
L = 6.0 m down a roof that is inclined at angle θ
= 30°.
(a) What is the angular speed of the cylinder about its center
as it leaves the roof?

A solid cylinder of radius 14 cm and mass 12 kg starts from rest
and rolls without slipping a distance of 6 m down a house roof that
is inclined 35 degrees. Refer to the figure below. What is the
angular speed of the cylinder just before it leaves the house
roof?

A hollow sphere of radius 16cm and mass 10kg stars from rest and
rolls without slipping a distance d=6.5m down a roof that is
inclined at an angle of 36°.
a. What is the angular speed of the hollow sphere about its
center as it leaves the roof?
b. The roof’s edge is at a height of 4.5m. How far horizontally
from the roof’s edge does the hollow sphere hit the level
ground?

A solid cylinder of mass 1.3 kg and radius 2.0 cm starts from
rest at some height above the ground and rolls down an ncline
without slipping. At the bottom of the incline, its linear speed is
2.5 m/s. (a) How much is its angular speed? (b) How much is its
rotational kinetic energy? The moment of inertia of a solid
cyllinder is 21mR2 (c) How much is its total energy at the bottom?
(d) From what height did it...

A solid cylinder starts rolling without slipping from
the top of an inclined plane. The cylinder starts moving from rest
at a vertical height 10m. The mass of the cylinder is 1kg and its
radius is .5m. The moment of inertia of the cylinder is 1/2
mr2 (where m is the mass of the cylinder and r is its
radius).
What is the speed of the center of mass of the
cylinder when its vertical height is 4 mm ?...

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...

A uniform, solid disk of mass M=4 kg and radius R=2 m, starts
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a) Derive the moment of inertia of the disk.
b) What is the linear speed of the ball when it leaves the
incline? Assume the ball rolls without slipping.

A solid cylinder starts rolling without slipping from the top of
an inclined plane. The cylinder starts moving from rest at a
vertical height 10m. The mass of the cylinder is 1kg and its radius
is .5m. The moment of inertia of the cylinder is 1/2 mr2
(where m is the mass of the cylinder and r is its radius).
1.What is the speed of the center of mass of the cylinder when
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A uniform, solid sphere of radius 3.00 cm and mass 2.00 kg
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Assuming the sphere rolls without slipping down the incline,
calculate the sphere's final translational speed v 2 at the bottom
of the ramp.

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