Question

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.

Answer #1

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 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.

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...

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 fixed at height h in the y-z plane with
the ability to rotate about its center. a mass is attached to a
point on the outside of the wheel by a string, causing it to rotate
clockwise. the S' frame is painted on the wheel and the system
itself is in the S frame. when the mass is released from rest S'
coincides with S. assuming that as the wheel rotates the S' frame...

.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.

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 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 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?...

in
the figure a rope is wrapped around a wheel of radius R= 2.0 m. the
moment of inertia if the wheel is 54 kg•m^2. the wheel is mounted
with frictionless bearings on an axle through its center. A block
of mass 14 kg is suspended from the end of the rope. when the
system is released from rest it is observed that the block descends
10 m in 2.0 sec. what is the speed of the block?

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