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 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?

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
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.

A hollow ball of mass 6.00 kg and radius 0.180 m is rolled up a
hill without slipping. If it starts off at the bottom with a linear
speed of 7.00 m/s, what vertical height (in m) will it reach?

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 hollow cylinder (hoop) of mass M and radius R starts rolling
without slipping (with negligible initial speed) from the top of an
inclined plane with angle theta. The cylinder is initially at a
height h from the bottom of the inclined plane. The coefficient of
friction is u. The moment of inertia of the hoop for the rolling
motion described is I= mR^2.
a) What is the magnitude of the net force and net torque acting
on the hoop?...

A sphere of radius r0 = 22.0 cm and mass m = 1.20kg starts from
rest and rolls without slipping down a 34.0 degree incline that is
12.0 m long.
Part A: Calculate its translational speed when it reaches the
bottom. (m/s)
Part B: Calculate its rotational speed when it reaches the
bottom. (rad/s)
Part C: What is the ratio of translational to rotational kinetic
energy at the bottom? (Ktr/Krot)
Part D: Does your answer in part A depend on...

a ball of mass M and radius R start from rest at a height of 5.0
m and rolls down a 20 degree slope as he fig below. what is the
linear speed of the ball when it leaves the incline? assuming that
the ball rolls without slipping B) a disk of M and radius R start
from rest at a height of 5.0 m and rolls down a 20 degree slope as
he fig below. what is the linear...

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