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.

.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?

A solid cylinder starts rolling without slipping from
the top of an inclined plane. The cylinder starts moving from rest
at a vertical height 10m. The mass of the cylinder is 1kg and its
radius is .5m. The moment of inertia of the cylinder is 1/2
mr2 (where m is the mass of the cylinder and r is its
radius).
What is the speed of the center of mass of the
cylinder when its vertical height is 4 mm ?...

7. A potter's wheel of radius 7.9 cm rotates with a period of
.44 s. What are a) the linear speed b) the centripetal acceleration
c) the angular velocity d) the angular acceleration of a small
clump of clay half way to the rim of the wheel?
8. A student sits at rost on a piano stool that can rotate
without friction. The moment of inertia of the student-stool system
is 6.3 kg m'. A second student tosses a 2.3...

A solid cylinder starts rolling without slipping from the top of
an inclined plane. The cylinder starts moving from rest at a
vertical height 10m. The mass of the cylinder is 1kg and its radius
is .5m. The moment of inertia of the cylinder is 1/2 mr2
(where m is the mass of the cylinder and r is its radius).
1.What is the speed of the center of mass of the cylinder when
its vertical height is 5 mm ?...

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