Question

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.

Answer #1

A sphere of radius r=34.5 cm and mass m= 1.80kg starts from rest
and rolls without slipping down a 30.0 degree incline that is 10.0
m long. calculate the translational and rotational speed when it
reaches the bottom.

A hollow ball of mass 2.88 kg and radius 0.309 m sits at rest on
top of a hill of height 6.88 m. The ball can either slide down the
hill without rolling or roll down without slipping. What is the
difference in the ball's speed (in m/s) at the bottom of the hill
between these two scenarios?

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 sphere of radius r0 = 23.0 cm and mass m = 1.20kg starts from
rest and rolls without slipping down a 35.0 ∘ incline that is 13.0
m long.
A. Calculate its translational speed when it reaches the
bottom.
B. Calculate its rotational speed when it reaches the
bottom.
C. What is the ratio of translational to rotational kinetic
energy at the bottom?

A sphere is released from the top of a rough inclined plane. The
friction is sufficient so that the sphere rolls without slipping.
Mass of the sphere is M and radius is R. The height of the center
of the sphere from ground is h. Find the speed of the center of the
sphere as it reaches the bottom of the sphere.

Two objects of equal mass m are at rest at the top of a hill of
height h. Object 1 is a circular hoop of radius r, and object 2 is
a solid disc, also of radius r. The object are released from rest
and roll without slipping.
A) Provide expressions for the LINEAR VELOCITY of each object
once it reaches the bottom of the hill. Careful - you should
provide two answers!
B) Considering your results from part A,...

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 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 sphere of radius r0 = 22.0 cm and mass m = 1.20kg starts from
rest and rolls without slipping down a 38.0 degree incline that is
11.0 mm long.
A. Calculate its translational speed when it reaches the
bottom.
B. Calculate its rotational speed when it reaches the
bottom.
C. What is the ratio of translational to rotational kinetic
energy at the bottom?
D. Does your answer in part A depend on mass or radius of the
ball?
E....

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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