Linear Momentum
b. This type of collision conserves momentum but does not conserve kinetic energy. This is often represented as a hit-and-stick problem.
b. Perfectly Inelastic Collision
A torque of 10 Nm is applied to a flywheel with a moment of inertia of 2 kg m^2. What is the angular acceleration of the flywheel?
5 rad/s^2
A spherical shell of mass 𝑚𝑚 = 2.00 kg and radius 𝑅𝑅 = 0.25 m is attached via a very light rod to a pivot point P. The distance between P and the center of mass is 3.00 m. What is the moment of inertia of the shell about the pivot point P?
I = 18.1 kg m^2
Solve: (4,5,2) * (-1,6,0)
26
a. If there is not net force on a particle, then the momentum of the particle must:
b. If two objects have equal kinetic energies, how do the magnitudes of their momenta compare?
a. Remain the same
b. Impossible to determine with given information
A 60-kg archer stands at rest on frictionless ice and fires a 0.030-kg arrow horizontally at 85 m/s. With what velocity does the archer move across the ice after firing the arrow?
v1f = -4.25 cm/s
A grinding wheel has an initial angular speed of 2000 rad/s and is slowing down due to a constant angular acceleration of -100 rad/s2. How long will it take for the wheel to come to rest?
20 seconds
An ice skater is spinning with their arms outstretched. When they pull their arms in, their angular velocity triples. By what factor does their moment of inertia change?
It decreased by a factor of 3
Cross Product Properties:
a. What is j x j?
b. What is j x k?
c. What is k x j?
a. j x j = 0
b. j x k = i
c. k x j = -i
A skater of mass m glides directly toward a pole with speed v. What is her angular momentum relative to the pole at the instant she is a distance d from the pole?
Zero
A car initially travelling at 15 m/s to the left collides with a wall. After the collision the car has a velocity of 2.6 m/s to the right. If the collision takes 0.15s and the car has a mass of 1500kg, what is the average force of the wall on the car?
Favg = 176000N
A pulley undergoes uniform angular acceleration about its center of mass of magnitude α = 30.0 rad/s2 from rest, reaching a maximum angular speed of ω = 2000 rad/s. What is the angular displacement during this process?
theta = 6.67e4 rad
The moment of inertia of a solid sphere is I = (2/5)MR^2. A 5 kg bowling ball with a radius of 11 cm will have how much angular momentum when it is rotating at 6 rad/s?
0.145 kg m^2/s
What can you say about the relationship between the magnitude of the cross product of two vectors and the product of the magnitudes of the vectors?
|A x B| could be less than or equal to AB
A table-tennis ball is thrown at a stationary bowling ball. The table-tennis ball makes a one-dimensional elastic collision and bounces back along the same line. Compared with the bowling ball after the collision, the table-tennis ball has
a smaller magnitude of momentum and more kinetic energy.
A block of mass m1 = 1.00 kg slides on a frictionless horizontal surface with a velocity of v1i = (3.00 𝒊̂) m/s. The mass then undergoes a perfectly inelastic collision with a block of mass m2 = 2.00 kg and velocity v2i = (−2.00 𝒊̂) m/s. What is the final velocity of the blocks?
-0.333 m/s
A force F=3i − 2j N is applied to a particle at a position r=4i +5j m relative to the origin. What is the torque τ acting on the particle about the origin?
torque = -23k N*m
Masses m1 and m2 are connected by a light cord that passes over a pulley. The pulley has a moment of inertia I and radius R. The masses are moving with speed v. What is the net torque on the system about the axle of the pulley?
m1gR k
Solve: (5,6,4) x (-8,-7,2)
(40, -42, 13)
a. Maximum torque occurs when a force is applied at this angle
b. If a force is applied directly toward the axis of rotation (the pivot), how much torque is produced?
a. 90 degrees
b. 0 N*m
A block of mass m1 = 2.00 kg moves with velocity v1i = (3.0 𝒋̂) m/s and collides elastically with another block of mass m2 = 1.00 kg at rest. Both mases move along the x-direction after the collision. What is the final velocity of m1?
v1f = 1i m/s
A child of mass m1 = 30.0 kg sits on a seesaw, 2.00 m from the pivot. If another child, of mass m2 = 40.0 kg, sits on the seesaw, how far from the pivot on the other side must they be for the seesaw to balance?
r = 1.5 m
A solid cylinder and a thin-walled hoop both have the same mass M and radius R. If they are released from rest at the top of an incline, which one has the larger moment of inertia about its central axis?
Thin-walled hoop
Theta = 20(1 - e-0.5t)
Find an equation for alpha in terms of t.
alpha = -5e-0.5t
A solid sphere and a hollow sphere have the same mass and radius. They are rotating with the same angular speed. Which one has the higher angular momentum?
the hollow sphere