Question

URGENT!!

a) A ball of radius ? and mass ? is rolling without slipping on the surface of a ring of radius ?. At a given instant, the ring is rotating with angular speed Ω counterclockwise as shown in the figure and the ball is rolling without slipping. What is the speed of the center of mass of the ball at that instant if it has clockwise angular speed of ω?

b)A yo-yo of mass ? has a spool of radius ? and an axle of radius of ?/2 (see the image below). Its moment of inertia about an axis passing through the center of the yo-yo can be approximated by ?0 = 1 2 ?? 2 . The yo-yo is placed on a horizontal surface, and the string is pulled with a force of magnitude ? in the direction shown in the figure. The axis of rotation of the yo-yo is perpendicular to the page. The downward acceleration of gravity is g. The coefficient of static friction between the yo-yo and the surface is ?? . What is the maximum magnitude of the pulling force, F, for which the yo-yo will roll without slipping?

Answer #1

A hollow sphere (mass 8.8 kg, radius 54.8 cm) is rolling without
slipping along a horizontal surface, so its center of mass is
moving at speed vo. It now comes to an incline that makes an angle
56o with the horizontal, and it rolls without slipping up the
incline until it comes to a complete stop. Find a, the magnitude of
the linear acceleration of the ball as it travels up the incline,
in m/s2.

A ball with a radius of 3.6 ?? is rolling without slipping and
is launched horizontally off of a table at 168 ??/ℎ. The ball hits
a wall that is 17.2 ? away, 433 ?? below the line it was projected
on. The ball has a constant deceleration of 11.5 ???/? 2 during the
flight to the wall. Determine, a. The number of revolutions the
ball makes during the flight. b. The angular speed when the ball
hits the wall.

7. We found that if a cue ball, rolling without slipping
at speed v0, strikes an identical, stationary billiard ball
head-on, eventually both balls will
roll without slipping. The balls are uniform solid spheres, each
of mass m, radius r, and
moment of inertia I =2/5 m r^2 about its center. The final speed
of the target ball is 5/7 *v0 ; that
of the cue ball is 2/7 v0. Calculate the total fraction of the
initial kenetic energy of...

.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 solid bowling ball with a mass of 6.8 kilograms is rolling
without slipping along a flat surface at a linear speed of 7.6 m/s.
The ball has a diameter of 8.5 inches. If instead of pins, it
encounters a long spring with a spring constant of 9300 N/m that
has been attached to a wall ahead of it, what is the maximum it can
compress the spring as it stops rolling.

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?...

Rotation (rolling without slipping)
Two cylinders with a radius r=0.650 m are rolled without slipping
down an incline that descends a vertical distance of 2.45 meters.
Each cylinder has equal mass m=3/68 kg, but one is solid and the
other is a hollow shell.
A) What is the center of mass velocity of the solid cylinder at the
bottom of the incline?
B) What is the center of mass velocity of the hollow cylinder at
the bottom of the incline?...

A wheel of radius R is rolling without slipping along a flat
surface. The center of the wheel is moving with the constant
horizontal velocity v.
a) Show that for the wheel not to slip, the angular velocity of
the wheel must be ω = v/R.
b) What is the velocity of a point on the wheel that is in
contact with the ground (Measured in a coordinate system on the
ground).
c) What is the velocity of a point...

A bicycle wheel of radius r is rolling without slipping with
constant speed Vo around a track with radius R (>>r). What is
the acceleration at the highest and lowest points of the wheel?
Choose the coordinate system with the origin at the center of the
wheen, rather than have the moving system rotate with the wheel,
choose the system which the z' axis points upward.

A solid sphere ( of mass 2.50 kg and radius 10.0 cm) starts
rolling without slipping on an inclined plane (angle of inclination
30 deg). Find the speed of its center of mass when it has traveled
down 2.00 m along with the inclination.
Groups of choices:
a. 3.13 m/s
b. 4.43 m/s
c. 3.74 m/s
d. 6.26 m/s

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