Question

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?

Answer #1

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A hollow sphere (mass M, radius R) starts from rest at the top
of a hill of height H. It rolls down the hill without slipping.
Find an expression for the speed of the ball's center of mass once
it reaches the bottom of the hill.

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?

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.

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 320-N sphere 0.20 m in radius rolls without slipping 6.0 m
down a ramp that is inclined at 34° with the horizontal. What is
the angular speed of the sphere at the bottom of the slope if it
starts from rest?

A hollow sphere (mass 8.8 kg, radius 54.8 cm) is rolling without
slipping along a horizontal surface, so its center of mass is
moving at speed vo. It now comes to an incline that makes an angle
56o with the horizontal, and it rolls without slipping up the
incline until it comes to a complete stop. Find a, the magnitude of
the linear acceleration of the ball as it travels up the incline,
in m/s2.

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 with mass M=4.2kg and radius R=0.25m rolls across
the floor without slipping. If the sphere has a totoal kinetic
energy of K=6.5J what is the angular speed?

3) A solid cylinder with mass 4kg and radius r=0.5 m rolls
without slipping from a height of 10 meters on an inclined plane
with length 20 meters. a) Find the friction force so that it rolls
without slipping b) Calculate the minimum coefficient of rolling
friction mu c) Calculate its speed as it arrives at the bottom of
the inclined plane

.A
uniform sphere of mass m radius r starts rolling down without
slipping from the top of another larger sphere of radius R. Find
the angular velocity of the sphere after it leaves the surface of
the larger sphere.

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