Question

Two spheres have the same radius (R) and same mass (M). One sphere is solid, and the other is hollow and made of a denser material. They start from rest at the top of an incline (rolls without slipping).

(a) Which has greater moment of inertia?

(b) Which has the greater rotational kinetic energy?

(c) Which has the greater total kinetic energy at the bottom?

(d) Which has the greater speed at the bottom?

(e) Given I solid shpere =(2/5) MR2 . What is its total kinetic energy?

Answer #1

Two spheres have the same radius (R) and same mass (M). One
sphere is solid, and the other is hollow and made of a denser
material. They start from rest at the top of an incline (rolls
without slipping).
(a) Which has greater moment of inertia?
(b) Which has the greater rotational kinetic energy?
(c) Which has the greater total kinetic energy at the
bottom?
(d) Which has the greater speed at the bottom?
(e) Given Isolid shpere =(2/5) MR2...

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...

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 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?

Q8
Two solid spheres of equal radius and equal mass start at rest at
the same height and move to the bottom of two different curved
ramps in two different ways.
In the first case (i), depicted in the left figure above, the ramp
has no friction so the sphere slides without rotating. In the
second case (ii), depicted in the right figure above, the sphere
rolls without slipping down the ramp.
In which case will the sphere have more...

Four objects with the same mass and radius roll without slipping
down an incline. If they all start at the same location, which
object will take the longest time to reach the bottom of the
incline? Mass Moment of Inertia Table Choices A. A hollow sphere B.
A solid sphere C. A thin-wall hollow cylinder D. They all take the
same time E. A solid cylinder

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 hollow sphere and a solid sphere each have the same mass and
radius. They are released simultaneously from rest and allowed to
roll without slipping down a ramp. Which one reaches the bottom
first? Group of answer choices
the solid sphere
You can't determine which is first unless you know the mass.
You can't determine which is first unless you know the
radius.
They reach the bottom at the same time.
the hollow sphere

A hollow sphere and a solid sphere each have the same mass and
radius. They are released simultaneously from rest and allowed to
roll without slipping down a ramp. Which one reaches the bottom
first?
Group of answer choices
You can't determine which is first unless you know the
radius..
You can't determine which is first unless you know the mass.
They reach the bottom at the same time.
the hollow sphere
the solid sphere

A solid sphere with a radius 0.25 m and mass 240 g rolls without
slipping down an incline, starting from rest from a height 1.0
m.
a. What is the speed of the sphere when it reaches the bottom of
the incline?
b. From what height must a solid disk with the same mass and
radius be released from rest to have the same velocity at the
bottom? It also rolls without slipping.

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