General Knowledge
If a spring with a force constant of 200 N/m is stretched 0.8 meters, what is its potential energy?
64 J
How much spring potential energy does a spring with k = 10 N/m have holding up a 1 kg mass?
4.8 J
If a kid is running with a speed of 3 m/s and jumps on the the edge of a merry-go-round with a radius of 2 m, what will their angular velocity be?
omega = 1.5 rad/s
What are the two forms of the torque formula?
tau = r x F
tau = rFsin(theta)
What is the formula for angular momentum?
L = Iw
What energy is required to raise 1 kg of mercury with a specific heat of 0.14 J/g*K, one degree celsius?
140 J
If I were to compress a spring(k = 5 N/m) a distance of 0.2 m with a mass of 2 kg, how high would the mass shoot up after releasing it?
h = 0.005 m
What is the moment of inertia of a system of point particles m1 = 2 kg, m2 = 5 kg, and m3 = 4 kg, with distances from the axis of rotation r1 = 2 m, r2 = 3 m, and r3 = 4 m?
I = 117 kgm2
How do you find the direction of torque using the right hand rule?
Use your right hand, point your fingers in the direction of r, curl your fingers towards F, and your thumb points in the direction of tau.
delta(L) = tau*delta(t)
If I spend $50 on my electric bill this month and my rate is $0.18 per kilowhatt, how much total energy did I use?
7.3e8 kJ
How much speed would a 2kg mass be moving with the instant it leaves a spring(k = 500 N/m) after compressing it 0.1 m?
v = 0.74 m/s
Explain, in words, how to derive moment of inertia for any object.
Cut up the object into small pieces, find an expression for the individual mass using ratio comparison to whole object, take the limit for infinitesimally small pieces, and integrate over the whole object.
Calculate the magnitude and direction of the torque when applying a force of <0, 30, 0> N at <2, 0, 0> m from the axis of rotation of an object.
tau = <0, 0, 60> N*m, pointing out of the page.
What does it mean that angular momentum is conserved?
delta(Lsys) + delta(Lsurr) = 0
Change in the angular momentum of the system must be equal and opposite to the change in angular momentum of the surroundings.
What is the cross product of A = <5, 3, 0> and B = <0, 2, -3>?
<-9, 15, 7>
How much would I need to compress a 5 meter spring(k = 1000 N/m) to launch a 5 kg object to a height of 40 meters?
s = 1.98 m
Calculate the moment of inertia of a uniform, thin rod where the axis of rotation is at a third of its length.
I = ML2/9
If a mass of 20 kg is sitting 1 m away from the pivot point of a seasaw, where must a 15 kg mass be set to keep the seasaw still?
1.5 m on the other side
Calculate the angular momentum of a thin rod of length 0.5 m and mass of 12 kg spinning about its center at 2.3 rad/s.
L = 0.58 kgm2/s
What is the center of mass of the following mass: m1 = 200 kg, r1 = <1, 0, 0>m, m2 = 300 kg, r2 = <0, 2, 0> m, and m3 = 500 kg, r3 = <-4, -5, 0>?
<-1.8, -1/9, 0>
How much would you need to compress a 40 meter spring(k = 50000 N/m) to launch a 20 kg mass to escape the atmosphere of a planet of mass 2.6x1013 kg, escape velocity of 230 m/s, and radius of 2.6x103 m?
s = 4.60 m
A system of two connected masses consists of a mass of 3 kg moving with a velocity of <3, 4, 0> m/s, and another mass of 5 kg moving with a velocity of <-1, 5, 0> m/s. What is the total, translational, and relative kinetic energy?
Ktrans = 86.6 J, Ktot = 102.5 J, Krel = 15.9 J
If a 2 m shelf is being held up by a perpendicular string on its right edge and is attached to a wall by a hinge on its left edge, what tension in the string will keep the shelf stable if it is holding a 10 kg mass at 2/3 of its length?
FT = 65.3 N
If a disk of 10 kg and radius of 0.3 m spins at 5 rad/s against another disk of 20 kg and a radius of 0.1 m so that it stops and only the second disk is moving, what speed is it moving at?
w = 0.9 rad/s