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Definition
| distance over time, delta d/delta t sometimes said as delta s/delta t |
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change in velocity over change in time.
Delta v / delta t |
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Mass of an object multiplied by it's acceleration.
m*a
F and a are vectors. |
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Work is the energy transferred to or from an object via the application of force along a displacement. Mathematically: Force multiplied by change in displacement distance.
F*s |
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Definition
The rate of change of the position angle of an object with respect to time.
w = delta theta / delta time
w = 2pi / T |
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Definition
Is the amount of energy transferred or converted per unit of time. This is basically work over change in time.
P = W (work) /delta t |
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Definition
Average power is the change in work over a change in time.
delta w / delta t |
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(Standard Equation)
Show the relationship of displacement: d to acceleration and original velocity. |
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Definition
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| Change in velocity in terms of acceleration. |
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Definition
| Delta_f v = delta_i v + a*t |
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Definition
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Definition
Angular momentum is a conserved quantity in a closed system. It is the rotational analog of linear momentum. It has both direction and a magnitude. It is found my multiplying mass * velocity * radius.
L = mvr |
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Definition
Is a quantity that is used in measuring a body's resistance to a change in its rotation direction or angular momentum. It tldr, characterizes the acceleration undergone by an object or solid when torque is applied.
I = L / w (angular velocity) |
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Definition
Momentum is the product of mass and velocity. It is a vector, having magnitude and direction.
p = mv |
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Definition
Impulse is just the change in momentum but given another name. It is the product of a constant force and elapsed time.
Delta p = F * delta t |
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| Moment of Inertia: I, in terms of mass. |
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Definition
I = sigma_i (m_i * (r_i)^2)
I = mr^2 |
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Definition
Kinetic friction is a frictional force opposing the motion of an object. Is the the product of coefficient of kinetic friction and the normal force.
f_k = u_k * F_n|N
(normal force can be found as either F_n or N.) |
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Definition
Normal force is the force the surface exerts on the object to prevent on another from passing through the other. This is the product of mass, gravity's acceleration, and the angle (if on an incline plane).
F_n = m * g * cos(theta) |
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Term
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Definition
Spring force is measuring the amount of force exerted on the spring to change it's position past it's point of equilibrium or rest position. It is the product of -1 with the spring force constant (k), and x being the position the spring is stretched from equilibrium. Spring constants are often expressed in N/m, Newton per meter.
F_spring = -k * x |
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Definition
Kinetic energy is the work needed to accelerate a body of mass from rest to a state velocity.
E_k = 1/2 * mv^2 |
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| Work done by a spring restoring itself to equilibrium: |
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Definition
product of one half of the spring constant (k) and distance of the compression of the spring (x).
W = 1/2 * kx^2 |
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| Work-Energy theorem: W_net |
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Definition
The net work done by the sum of all forces acting on a particle is equal to the change in kinetic energy of that particle.
W_net = E_kfinal + E_kinital |
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Do not solve, but indicate the steps taken to solve this problem.
[image][image] |
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Definition
| Firstly we'd start with the spring constant -> work -> kinetic energy -> velocity -> now we'd solve the slop's net forces -> perpendicular force aka normal force on a 45 degree slope -> we'd find the parallel force aka friction leveraging normal force found previously -> we'd equate net force and distance traveled to work -> Using work energy theorem we'd compare kinetic energy right before slope to after the slope finding velocity at the end of the slope -> now we'd find the distance travelled after the slope -> finding the Vi * Vj of the velocity. Finding v_y we could use some algebra to solve for y at 0 to find total time in the air -> using time that was just found we could find the distance traveled along the x-axis. This would result in total distance. |
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| Inertia of a body about an axis: I |
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Definition
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| Velocity: V, in terms of angular velocity |
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Definition
w is angular velocity and r is distance from axis.
v = wr |
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| Angular Velocity: w (omega), in terms of velocity v. |
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Definition
If the angular velocity is positive, the velocity will be negative. The quotient of velocity in the x direction and radius.
w = - v_x / r |
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| Power: P, in terms of of kinetic energy E_k. |
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Definition
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Term
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Definition
Rotational equivalent of force.
Torque is a measure of the force that can cause an object to rotate about an axis.
It describes the rate of change of angular momentum that would be imparted to an isolated body.
"Torque measures the "effectiveness" of the force at causing an object to rotate about a pivot."
It is the product of radius or distance from point of pivot (r), force (F), and angle where the force is applied (sin(theta)).
Units: Newton-meters (N m),
Note: We said 1N m is equal to 1 J when discussing energy but torque is not an energy related quantity so we do not use Joules.
t (tau) = r*F*sin(theta)
[image] |
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Term
| Perfectly inelastic collisions |
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Definition
A collision where two objects stick together sharing a common velocity after the collisions.
In this momentum is conserved whilst mechanical energy is not. |
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| Perfectly elastic collision |
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Definition
In this scenario two forces collide and separate conserving both mechanical energy and momentum.
P_f = P_i
E_mf = E_mi |
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| Centripetal Acceleration: a_c |
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Definition
Is the acceleration of an object moving in uniform circular motion. It is the quotient of velocity squared (v^2) and radius from center (r).
a_c = v^2 / r |
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| Angular acceleration: a, in terms of net torque and moment of inertia. |
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Definition
Quotient of net torque (t_net (tau)) and moment of inertia (I) about the rotation axis.
a = (t_net (tau)/ I)
Unit: rad/s^2
We also use this rule to write t_net = I*a |
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Definition
Torque, moment of inertia, angular acceleration, Newton's second law.
t_net (tau), I, a, a = t_net* I |
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Definition
Force (N), mass (kg), acceleration (m/s^2), second law.
F_net (vector), m, a (vector), a (vec) = F_net (vec) * m |
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| Problem-Solving Strategy: Rotational dynamics problems. |
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Definition
Model, Visualize, Solve, Assess.
[image] |
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| Static Equilibrium: "statics" |
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Definition
An extended object thatt is completely stationary is said to be in static equilibrium.
It has no linear accerlation nor angular acceleration. Using Newton's second law there are no net force or net toque upon the object.
This is the basis of a branch of engineering called statics. |
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Definition
Where Net Force equals zero.
F_net = 0 |
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Definition
Where net torque is equal to zero.
t_net (tau) = 0 |
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Definition
A cross product is the product of two vectors and was seen in rotational motion chapter, it looks like an "x" symbol between A(vector) & B(vector)
Does not obey the commutative rule (ab = ba)
A x B |
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Definition
This is a rule that aids in knowing which way torque as a vector will point. It will always be perpendicular to the plane of A and B but which direction changes upon r and F.
[image] |
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| Angular momentum: L(vector) |
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Definition
It is the cross product of position (s) and momentum (p(vector) = m*v(vector))
Unit: kg m^2/s
L(vector) = r(vector) x (cross product) p(vector)
OR
L(vector) = m(mass)*r(position)*v(velocity)*sin(angle of p to r) |
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| Angular velocity: w (omega) |
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Definition
Is the quotient of change to change to angular velocity and change in time.
a = theta w * theta t |
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Term
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Definition
Is the sum of inertia, angular acceleration, and time.
L = Iat |
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| Question: When angular momentum is constant what does this mean for net torque on the system? |
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Definition
| The net torque on the system will = 0. This is due to the fact the angular momentum is conserved when net torque is zero. Mathmaticaly dL / dt = t_net (torque) |
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| Translational kinetic energy to rotational. |
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Definition
Translational: 1/2 m*v^2
Rotational: 1/2 m*w^2, where w = velocity / radius |
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| Newton's Law of Universal Gravitation: F_g |
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Definition
Two bodies exert gravitational forces upon each other of equal force. It is the product of, m_1 & m_2 (mass of both objects) and G (universal gravitational constant) and quotient of this over r^2 (distance between the two center's of the objects.)
F_g = (G * m_1, m_2)/ r^2 |
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| Potential Energy in terms of gravity: U |
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Definition
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| Gravity Speed of an object: S |
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Definition
| S = sqrt(2G(M_larger object)) / R) |
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Definition
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| Kinetic Energy as a function of time to velocity as a function of time. |
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Definition
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