Question

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?

Answer #1

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 sphere of radius r and mass m is released from a rest on
a track. At a height h above a horizontal surface. The sphere rolls
without slipping with its motion continuing around a loop of radius
R<<r
A) If R=0.3h, what is the speed of the sphere when it reaches
the top of the loop? Your response must be expressed in terms of
some or all of the quantities given above and physical and
numerical constants
B)...

A hollow sphere of radius 0.120 m, with rotational inertia
I = 0.0612 kg·m2 about a line through its
center of mass, rolls without slipping up a surface inclined at
33.8° to the horizontal. At a certain initial position, the
sphere's total kinetic energy is 42.0 J. (a) How
much of this initial kinetic energy is rotational?
(b) What is the speed of the center of mass of the
sphere at the initial position? When the sphere has moved 0.610...

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 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 Brunswick bowling ball with mass M= 7kg and radius R=0.15m
rolls from rest down a ramp without slipping. The initial height of
the incline is H= 2m. The moment of inertia of the ball is
I=(2/5)MR2
What is the total kinetic energy of the bowling ball at the
bottom of the incline?
684J
342J
235J
137J
If the speed of the bowling ball at the bottom of the incline is
V=5m/s, what is the rotational speed ω at the...

A hollow sphere of radius 0.24 m, with rotational inertia
I = 0.036 kg · m2 about a line through its
center of mass, rolls without slipping up a surface inclined at 29°
to the horizontal. At a certain initial position, the sphere's
total kinetic energy is 25 J.
(a) How much of this initial kinetic energy is rotational?
_________ J
(b) What is the speed of the center of mass of the sphere at the
initial position?
_________m/s
Now,...

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 nonuniform cylinder (radius = 0.14 m, center-of-mass
rotational inertia = 2.22×10-2 kg·m2, mass = 1.33 kg) starts from
rest and rolls without slipping down a plane with an angle of
inclination of 24.2°. How long does it take to travel 1.56 m along
the incline?

A solid sphere of a radius 0.2 m is released from rest from a
height of 2.0 m and rolls down the incline as shown. If the initial
speed Vi= 5 m/s, calculate the speed (Vf) of the sphere when it
reaches the horizontal surface. (moment of inertia of a sphere is
(2/5) Mr^)

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