Question

A 350-N sphere 0.20 m in radius rolls without slipping 6.0 m down a ramp that is inclined at 25° with the horizontal. What is the angular speed of the sphere at the bottom of the slope if it starts from rest? rad/s

Answer #1

from energy coservation

[ rotational kinetic energy + translational energy + potentional
energy ]_{top} =[ rotational kinetic energy + translational
energy + potentional energy ]_{bottom}

**at top**

rotational kinetic energy = 0 since at rest on top

translational energy = 0

and potentional energy =

**at bottom**

rotational kinetic energy =

translational energy =

potentional energy = 0;

since no slipping

and

so from energy conservation :

so here we take g = 9.81 m/s^2

m/s

so angular velocity from

A 340-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?
in rad/s

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 solid, uniform sphere of mass 2.0 kg and radius 1.7m rolls
without slipping down an inclined plane of height 7.0m . What is
the angular velocity of the sphere at the bottom of the inclined
plane? a) 5.8 rad/s b) 11.0 rad/s c) 7.0 rad/s d) 9.9 rad/s

A uniform disc of mass M=2.0 kg and radius R=0.45 m rolls
without slipping down an inclined plane of length L=40 m and slope
of 30°. The disk starts from rest at the top of the incline. Find
the angular velocity at the bottom of the incline.

A solid cylinder rolls without slipping down a 30° incline that
is 5.0 m long. The cylinder's mass is 3.0 kg and its diameter is 44
cmcm . The cylinder starts from rest at the top of the ramp.
1) What is the linear speed of the center of the cylinder when
it reaches the bottom of the ramp.
2) What is the angular speed of the cylinder about its center at
the bottom of the ramp.
3) What is...

A solid, uniform disk of radius 0.250 m and mass 54.1 kg rolls
down a ramp of length 3.80 m that makes an angle of 12.0° with the
horizontal. The disk starts from rest from the top of the ramp.
(a) Find the speed of the disk's center of mass when it reaches
the bottom of the ramp.
___________m/s
(b) Find the angular speed of the disk at the bottom of the
ramp.
___________rad/s

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.

A very thin circular hoop of mass m and radius
r rolls without slipping down a ramp inclined at an angle
θ with the horizontal, as shown in the figure.
What is the acceleration a of the center of the
hoop?

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 basketball starts from rest and rolls without slipping down a
hill. The radius of the basketball is 0.23 m, and its 0.625 kg mass
is evenly distributed in its thin shell. The hill is 50 m long and
makes an angle of 25° with the horizontal. How fast is it going at
the bottom of the hill?
Group of answer choices
10.7 m/s
12.3 m/s
15.8 m/s
14.4 m/s
17.2 m/s

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