Question
In: Physics
A machine part has the shape of a solid uniform sphere of mass 220 g and...
A machine part has the shape of a solid uniform sphere of mass 220 g and diameter 2.90 cm . It is spinning about a frictionless axle through its center, but at one point on its equator it is scraping against metal, resulting in a friction force of 0.0200 N at that point.
Part A
Find its angular acceleration. Let the direction the sphere is spinning be the positive sense of rotation.
Part B
How long will it take to decrease its rotational speed by 19.0 rad/s ?
Solutions
Expert Solution
Mass of the solid uniform sphere = M = 220 g = 0.22 kg
Diameter of the solid uniform sphere = D = 2.9 cm = 0.029 m
Radius of the solid uniform sphere = R = D/2 = 0.029/2 = 0.0145 m
Moment of inertia of the solid uniform sphere = I
I = 1.85 x 10-5 kg.m2
Friction force on the sphere = F = 0.02 N
The sphere is being scraped at the equator therefore the distance of the friction force from the axis of rotation is equal to the radius of the sphere.
Torque on the sphere due to the friction force = 
= -FR (Negative as the torque is acting in the opposite direction
of the motion of the sphere)
= -(0.02)(0.0145)
= -2.9 x 10-4 N.m
Angular acceleration of the sphere = 
= -15.7 rad/s2
Time taken to reduce the rotational speed of the sphere by 19 rad/s = t
Change in angular speed of the sphere = 
= -19 rad/s (Negative as it has decreased)
t = 1.21 sec
A) Angular acceleration of the sphere = -15.7 rad/s2
B) Time taken to reduce the rotational speed of the sphere by 19 rad/s = 1.21 sec
genius_generous answered 10 months agoRelated Solutions
A frictionless pulley has the shape of a uniform solid disk of mass 6.00 kg and...
A frictionless pulley has the shape of a uniform solid disk of
mass 6.00 kg and radius 12.0 cm . A 3.60 kg stone is attached to a
very light wire that is wrapped around the rim of the pulley(Figure
1), and the stone is released from rest. As it falls down, the wire
unwinds without stretching or slipping, causing the pulley to
rotate. How far must the stone fall so that the pulley has 7.50 J
of kinetic energy?
2. Which has more rotational inertia: A solid, uniform sphere of mass 100kg, or a mostly...
2. Which has more rotational inertia: A solid, uniform sphere of
mass 100kg, or a mostly hollow spherical shell of mass 100kg?
a.They both have the same rotational inertia
b.Solid Sphere
c.Hollow Sphere
3.If a bicycle starts from rest and is pedaled normally until
the bike is moving at 6 meters per second across level ground, what
kinds of energy have its tires been given? (Select all that
apply)
a.Rotational Kinetic Energy
b.Translational Kinetic Energy
c.Gravitational Potential Energy
d.Elastic Potential...
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is...
A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
Read it to me
R F U R or U F or U R or...
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is...
A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
The new sphere has mass M = M0 and radius R >
R0
The new...
A small solid sphere of mass M0, of radius R0, and of uniform density ?0 is...
A small solid sphere of mass M0, of radius
R0, and of uniform density ?0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
Read it to me
R F U R or U F or U R or...
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is...
A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
The new sphere has mass M = M0 and density ρ <
ρ0
The new...
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is...
A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
R F U R or U F or U R or F or U The new...
A small solid sphere of mass M0, of radius R0, and of uniform density ρ0 is...
A small solid sphere of mass M0, of radius
R0, and of uniform density ρ0 is placed in a
large bowl containing water. It floats and the level of the water
in the dish is L. Given the information below, determine the
possible effects on the water level L, (R-Rises, F-Falls,
U-Unchanged), when that sphere is replaced by a new solid sphere of
uniform density.
Read it to me
R F U R or U F or U R or...
A uniform brass solid cylinder has a mass, m = 500 g, and a diameter, D...
A uniform brass solid cylinder has a mass, m = 500 g, and a
diameter, D = 6 cm and a length L = 1 m. The cylinder rotates about
its axis of rotational symmetry at an angular velocity of 60
radians/s on a frictionless bearing.
(a) What is the angular momentum of the cylinder?
(b) How much work was required to increase the angular momentum
of the cylinder to this value if the cylinder was initially at
rest? Once...
Attempt 4 A uniform, solid sphere of radius 5.50 cm and mass 1.25 kg starts with...
Attempt 4 A uniform, solid sphere of radius 5.50 cm and mass
1.25 kg starts with a purely translational speed of 3.25 m/s at the
top of an inclined plane. The surface of the incline is 2.50 m
long, and is tilted at an angle of 34.0∘ with respect to the
horizontal. Assuming the sphere rolls without slipping down the
incline, calculate the sphere's final translational speed ?2 at the
bottom of the ramp.
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- As of 2015, ranches were taxed at 13 percent for income up to $42,000; at 20...
- Do you think that questionnaires or interviews provide more data?
- Lindsey was recently hired by Swift Ltd. as a junior budget analyst. She is working for...
- a laboratory-scale stirred tank fermenter of volume 51 (do/h=1/2) is to be scaled up to 500l...
- String search Describe the brute force solution to counting the number of times the letter “a”...
- (Hedging principle) A popular theory for managing risk to the firm that arises out of its...
- Biomaterial Interface Question List and briefly describe 5 design features you could incorporate in the design...
ADVERTISEMENT