A uniform solid sphere of radius r = 0.420 m and mass m = 13.5 kg turns counterc
ID: 2032637 • Letter: A
Question
A uniform solid sphere of radius r = 0.420 m and mass m = 13.5 kg turns counterclockwise about a vertical axis through its center (when viewed from above). Find its vector angular momentum about this axis when its angular speed is 2.9 rad/s.
--Direction-- upward downward clockwise counterclockwise
A uniform solid disk of mass m = 2.95 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.06 rad/s.
(a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass.
kg · m2/s
(b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim?
kg · m2/s
A puck of mass m = 51.0 g is attached to a taut cord passing through a small hole in a frictionless, horizontal surface (see figure below). The puck is initially orbiting with speed vi = 1.70 m/s in a circle of radius ri = 0.290 m. The cord is then slowly pulled from below, decreasing the radius of the circle to r = 0.130 m.
(a) What is the puck's speed at the smaller radius?
m/s
(b) Find the tension in the cord at the smaller radius.
N
(c) How much work is done by the hand in pulling the cord so that the radius of the puck's motion changes from 0.290 m to 0.130 m?
J
A projectile of mass m moves to the right with a speed vi. The projectile strikes and sticks to the end of a stationary rod of mass M, length d, pivoted about a frictionless axle perpendicular to the page through O. We wish to find the fractional change of kinetic energy in the system due to the collision.
(a) What is the appropriate analysis model to describe the projectile and the rod?
isolated systemnon-isolated system
(b) What is the magnitude of the angular momentum of the system before the collision about an axis through O? (Use the following as necessary: m, vi, M, and d.)
Ltotal =
(c) What is the moment of inertia of the system about an axis through O after the projectile sticks to the rod? (Use any variable or symbol stated above as necessary.)
Itotal =
(d) If the angular speed of the system after the collision is ?, what is the magnitude of the angular momentum of the system after the collision? (Use the following as necessary: m, ?, M, and d.)
Ltotal =
(e) Find the angular speed ? after the collision in terms of the given quantities. (Use any variable or symbol stated above as necessary.)
? =
(f) What is the kinetic energy of the system before the collision? (Use any variable or symbol stated above as necessary.)
K =
(g) What is the kinetic energy of the system after the collision?
Ktotal =
(Use any variable or symbol stated above as necessary.)
(h) Determine the fractional change of kinetic energy due to the collision. (Use any variable or symbol stated above as necessary.)
=
magnitude kg · m2/s direction--Direction-- upward downward clockwise counterclockwise
A uniform solid disk of mass m = 2.95 kg and radius r = 0.200 m rotates about a fixed axis perpendicular to its face with angular frequency 6.06 rad/s.
(a) Calculate the magnitude of the angular momentum of the disk when the axis of rotation passes through its center of mass.
kg · m2/s
(b) What is the magnitude of the angular momentum when the axis of rotation passes through a point midway between the center and the rim?
kg · m2/s
A puck of mass m = 51.0 g is attached to a taut cord passing through a small hole in a frictionless, horizontal surface (see figure below). The puck is initially orbiting with speed vi = 1.70 m/s in a circle of radius ri = 0.290 m. The cord is then slowly pulled from below, decreasing the radius of the circle to r = 0.130 m.
(a) What is the puck's speed at the smaller radius?
m/s
(b) Find the tension in the cord at the smaller radius.
N
(c) How much work is done by the hand in pulling the cord so that the radius of the puck's motion changes from 0.290 m to 0.130 m?
J
A projectile of mass m moves to the right with a speed vi. The projectile strikes and sticks to the end of a stationary rod of mass M, length d, pivoted about a frictionless axle perpendicular to the page through O. We wish to find the fractional change of kinetic energy in the system due to the collision.
(a) What is the appropriate analysis model to describe the projectile and the rod?
isolated systemnon-isolated system
(b) What is the magnitude of the angular momentum of the system before the collision about an axis through O? (Use the following as necessary: m, vi, M, and d.)
Ltotal =
(c) What is the moment of inertia of the system about an axis through O after the projectile sticks to the rod? (Use any variable or symbol stated above as necessary.)
Itotal =
(d) If the angular speed of the system after the collision is ?, what is the magnitude of the angular momentum of the system after the collision? (Use the following as necessary: m, ?, M, and d.)
Ltotal =
(e) Find the angular speed ? after the collision in terms of the given quantities. (Use any variable or symbol stated above as necessary.)
? =
(f) What is the kinetic energy of the system before the collision? (Use any variable or symbol stated above as necessary.)
K =
(g) What is the kinetic energy of the system after the collision?
Ktotal =
(Use any variable or symbol stated above as necessary.)
(h) Determine the fractional change of kinetic energy due to the collision. (Use any variable or symbol stated above as necessary.)
=
Explanation / Answer
1.
Moment of inertia of solid sphere is given by:
I = 2*M*R^2/g
Angular momentum is given by:
L = I*w
L = 2*M*R^2*w/5
Using given values:
L = 2*13.5*0.420^2*2.9/5
L = 2.76 kg-m^2/sec
Since the sphere is rotating CCW bout vertical axis, So direction = upward
Q2A
Again L = I*w
for solid disk, when axis of rotation passes through COM
I = M*R^2/2
L = M*R^2*w/2
L = 2.95*0.2^2*6.06/2
L = 0.357 kg-m^2/sec
Q2B
for solid disk, when axis of rotation passes through a point midway between the center and the rim
I1 = M*R^2/2 + M*(R/2)^2 = 3*M*R^2/4
L1 = I1*w
L1 = 3*M*R^2*w/4
L1 = 3*2.95*0.2^2*6.06/4
L1 = 0.536 kg-m^2/sec
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