Question

.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.

Answer #1

In the equilibrium, the centripetal force must be equal to the down word force.

So,

*mv*^{2}/(*R*+*r*) = *mg*
cos*?*

When the body is rolling without slipping, in accordance to principle of conservation of energy, potential energy must be in the form of translational energy plus rotational kinetic energy.

So,

*mgh* = ½ *mv*^{2} + ½
*I?*^{2}

Or,

*mg*(*R*+*r*) (1-cos*?*) = ½
*mv*^{2}+(1/5 )*mv*^{2}

= (7/10) *mv*^{2}

Or,

(10/7) *mg* (1-cos*?*) = *mg*
cos*?*

Again,

*mv*^{2} = (10/7) *mg*
(*R*+*r*) (1-cos*?*)

10/7 = 17/7 cos*?*

Or, cos*?* = 10/17

The velocity of sphere radius *r* at the instant when it
leaves contact with surface of fixed sphere will be,

*v* = v[*g*(*R*+*r*) cos*?*]
=v[(10/17){*g*(*R*+*r*)}]

So the angular velocity will be,

*?* = *v*/*r*

=v[(10/17*r*^{2}){*g*(*R*+*r*)}]

From the above observation, we conclude that, the angular
velocity of sphere radius *r* at the instant when it leaves
contact with surface of fixed sphere would
bev[(10/17*r*^{2}){*g*(*R*+*r*)}]
.

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 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.

A
sphere of radius 10 m and a mass m1 = 5 kg is rolling without
slipping on a horizotal surface with a velocity V = 20 m/s to the
East. It collides with a stationery sphere of mass m2 =15 kg. After
the collision both masses rolls in different directions and m1 with
a velocity V = 5 m/s.
1) Find the velocity of m2 after collision
2) Find the angular velocity of m2 after the collision
3) Was...

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

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 uniform, solid sphere of radius 3.00 cm and mass 2.00 kg
starts with a purely translational speed of 1.25 m/s at the top of
an inclined plane. The surface of the incline is 1.00 m long, and
is tilted at an angle of 25.0 ∘ with respect to the horizontal.
Assuming the sphere rolls without slipping down the incline,
calculate the sphere's final translational speed v 2 at the bottom
of the ramp.

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 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

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 solid sphere with mass M=4.2kg and radius R=0.25m rolls across
the floor without slipping. If the sphere has a totoal kinetic
energy of K=6.5J what is the angular speed?

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 13 minutes ago

asked 13 minutes ago

asked 14 minutes ago

asked 21 minutes ago

asked 32 minutes ago

asked 32 minutes ago

asked 33 minutes ago

asked 34 minutes ago

asked 40 minutes ago

asked 49 minutes ago

asked 53 minutes ago

asked 54 minutes ago