A
Does the cross product commute (Meaning: is A x B = B x A)?
No, A x B = -B x A
What must be true for the acceleration in order for the kinematics equations to hold?
The acceleration must be constant.
What is the difference between average acceleration and instantaneous acceleration? And what are the formulas for each?
average acceleration: the rate of change in velocity; the change in velocity over time (delta v/delta t)
instantaneous acceleration: acceleration at a specific point in time (dv/dt)
Can instantaneous velocity be negative? What about instantaneous speed?
Instantaneous velocity is a vector and can be negative.
Instantaneous speed is found by taking the absolute value of instantaneous velocity, and it is always positive.
What is centripetal acceleration? And what is its magnitude?
Component of acceleration of an object moving in a circle that is directed radially inward toward the center of the circle, a = v2/r
If an object has a constant x-component of the velocity and suddenly experiences an acceleration in the y direction, does the x-component of its velocity change?
No, motions in perpendicular directions are independent.
If two reference frames are moving relative to each other at a constant velocity, then what is true for the acceleration that is observed?
The accelerations of an object as observed in both reference frames are equal.
A rock is thrown straight up. At the top of the trajectory, the velocity is momentarily zero. Does this imply that the force acting on the object is zero? Explain your answer.
No. If the force were zero at this point, then there would be nothing to change the object’s momentary zero velocity. Since we do not observe the object hanging motionless in the air, the force could not be zero.
What is Hooke's Law?
in a spring, a restoring force proportional to and in the opposite direction of the imposed displacement, F = -kx
What condition about air resistance must be true in order for an object in free fall to experience constant acceleration?
Air resistance is negligible
What is the physical meaning of a non-conservative force? And what does it mean for the work done?
Non-conservative force: A force that takes energy away from the system that can’t be recovered if we were to reverse the action.
A conservative force is one for which the work done is independent of path (for non-conservative forces we need to care about the path taken). Equivalently, a force is conservative if the work done over any closed path is zero.
What is viscosity?
measure of the internal friction in a fluid
Is it possible for speed to be constant while acceleration is not zero?
No, in one dimension constant speed requires zero acceleration.
State Archimedes' Principle
buoyant force on an object equals the weight of the fluid it displaces
If there is an odd number of forces act on an object, can the object be in equilibrium?
Yes, provided forces add to zero as vectors then equilibrium can be achieved.
Equilibrium means that the net force and the net torque equals zero.
A physics major is cooking breakfast when she notices that the frictional force between her steel spatula and Teflon frying pan is only 0.200 N. Knowing the coefficient of kinetic friction = 0.04 between the two materials, she quickly calculates the normal force. What is it?
Normal force = 0.2/0.04 = 5 N
Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point and what is the compass direction of a line connecting your starting point to your final position?
30.81 m
54.25 degrees west north
A clock is mounted on the wall. As you look at it, what is the direction of the angular velocity vector of the second hand?
The second hand rotates clockwise, so by the right-hand rule, the angular velocity vector is into the wall.
The angular velocity is found using the right-hand rule. If the fingers curl in the direction of rotation about a fixed axis, the thumb points in the direction of the angular velocity.
A child jumps up and down on a bed, reaching a higher height after each bounce. Explain how the child can increase his maximum gravitational potential energy with each bounce.
He puts energy into the system through his legs compressing and expanding.
An object that is thrown straight up falls back to Earth. This is one-dimensional motion. (a) When is its velocity zero? (b) Does its velocity change direction? (c) Does the acceleration have the same sign on the way up as on the way down?
a. at the top of its trajectory; b. yes, at the top of its trajectory; c. yes
As the rope of a tethered ball winds around a pole, what happens to the angular velocity of the ball?
The angular velocity increases because the moment of inertia is decreasing. (conservation of angular momentum problem)
How is pressure related to the sharpness of a knife and its ability to cut?
(Hint: start by giving the formula for pressure)
Pressure is force divided by area. If a knife is sharp, the force applied to the cutting surface is divided over a smaller area than the same force applied with a dull knife. This means that the pressure would be greater for the sharper knife, increasing its ability to cut.
As a young man, Tarzan climbed up a vine to reach his tree house. As he got older, he decided to build and use a staircase instead. Since the work of the gravitational force mg is path independent, what did the King of the Apes gain in using stairs?
Both require the same gravitational work, but the stairs allow Tarzan to take this work over a longer time interval and hence gradually exert his energy, rather than dramatically by climbing a vine.
If a particle is moving with respect to a chosen origin it has linear momentum. What conditions must exist for this particle’s angular momentum to be zero about the chosen origin?
angular momentum = r x p
The particle must be moving on a straight line that passes through the chosen origin.
All points on the straight line will give zero angular momentum, because a vector crossed into a parallel vector is zero.
State Newton's three laws of motion.
Newton’s first law of motion: body at rest remains at rest or, if in motion, remains in motion at constant velocity unless acted on by a net external force; also known as the law of inertia
Newton’s second law of motion: acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system and is inversely proportional to its mass
Newton’s third law of motion: whenever one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction to the force that it exerts