Vector Magnitude & Uniform Circular Motion – Physics
This Physics chapter is about Vector Magnitude & Uniform Circular Motion.
Can the magnitude of the displacement vector be more than the distance traveled?
No
Can the magnitude of the displacement vector be less than the distance traveled?
yes
Suppose two vectors have unequal magnitudes. Can their sum be zero?
No
The magnitude of a vector can be different in different coordinate systems. (true or false)
false
The direction of a vector can be different in different coordinate systems. (true or false)
false
The components of a vector can be different in different coordinate systems. (true or false)
true
Fundamental Units
Length (l) Time (t) Mass (M)
Length
meter-accepted unit
time
second-accepted unit
minutes
hours
mass
kilogram-accepted unit
pound
Velocity equation
length/ time
acceleration equation
length/ time^2
Force equation
(mass x length)/ (time x time)
How many cm does 1 inch equal
2.54 cm
how many ft is equivalent to 1 m
3.28 ft
how many feet is equivalent to 1 mile
5280 ft
how many kilometers (km) are in a mile
1.61 km
Quantities have a ______ and a _______
size number, physical unit
Scalar Quantities
have only magnitude
Vector Quantities
have both magnitude and direction
“weakest link” rule
The input number with the smallest number of significant figures determines the number of significant figures to use in the output value
If the number before 5 is odd
Round up
if the number before 5 is even
let it be
Displacement
change in position from your starting point to end point
Average Velocity
the average velocity of an object during a time interval (delta t) in which the object undergoes a displacement (delta r ) is the vector: Vavg= (delta r vector)/(delta t)
Acceleration describes a _______ in velocity
change
Average Acceleration
The rate of change of velocity
Aavg= (delta V)/ (delta t)
Kinematics
the study of motion
the motion of an object is described by its; ____________, ______________, ________________
position, velocity, acceleration
Instantaneous Velocity
the velocity at one particular instant in time, not an average. This is what your car speedometer reads.
The instantaneous velocity is equivalent to ______________
the slope of the tangent line
Motion Diagram
shows the position of a particle at various instants, and arrows represent its velocity at each instant
The total displacement
area under the curve
Can you find instantaneous acceleration and average acceleration from an velocity time graph?
Yes
Slope of the tangent line to the velocity time curve at a given point is equal to?
The instantaneous acceleration at that point
the steeper the slope (positive or negative) of an objects velocity time graph the _________________ is the objects acceleration in the positive or negative x-direction.
Greater
You run around a circular track at a constant speed. Which of these statements is true?
a. Your velocity is constant, your acceleration is zero
b. your velocity is constant, your acceleration is not zero
c. your velocity is changing, your acceleration is zero
d. your velocity is changing, your acceleration is not zero – correct
Motion with constant velocity and zero acceleration is________________
Uniform Motion
The motions of a car and a truck along a straight road are represented by the velocity-time graphs in the figure. The two vehicles are initially alongside each other at time t=0. At time T, what is true about these two vehicles since time t=0?
a. the car will be moving faster than the truck
b. the car will have traveled further than the truck
c. the truck will have traveled further than the car – correct
d. the truck and the car will have traveled the same distance
Instantaneous Velocity equals the slope of the _______________ graph
position
Instantaneous Acceleration equals the slope of the ________ graph
velocity
Two objects dropped from the same height will, if air resistance neglected, hit the ground at _____________________ time and with the __________________ speed
same, same
Any two objects in free fall, regardless of their mass have the same ___________________
acceleration
g is a ___________ number
positive
g =
9.80 m/s^2
A quantity that is fully described by a single number is called a __________
scalar quantity
Two new vectors parallel to the axes are called ______________
component vectors
a ________________ has a magnitude of 1 with no units
Unit vectors
You fly east in an airplane for 100 km. You then turn left 60 degrees and fly 200 km. What is the magnitude of your displacement?
a. 170 km
b. 200 km
c. 260 km – correct
d. 300 km
Is an object still considered in free fall if it is moving upward?
yes
A coin is dropped and falls for 1 second before hitting the ground. How high up was the coin when it was dropped?
a. 1m
b. 5m – correct
c. 10m
d. 15m
A ______________ is any object that is given an initial velocity and then follows a path (trajectory) determined solely by gravity and air resistance
Projectile
Horizontal motion will have __________ acceleration and thus have ____________ velocity
zero, constant
Vertical Motion will have _______________________ downward acceleration of magnitude
constant
A car is traveling around a curve at a steady 45 mph. Is the car accelerating?
Yes
____________________ is the rate at which a particles angular position is changing
Angular Velocity
In uniform circular motion, although the speed is constant, there is ______________ because the direction of the velocity vector is always changing.
acceleration
_______________________ is the acceleration of uniform circular motion
centripetal acceleration
Convert to SI Units
13 in
.33 m
Convert to SI units
70ft/s
21m/s
Convert to SI units
78 mph
35m/s
Convert to SI units
15 in^2
9.7×10^-3m^2
The position x, in meters, of an object is given by the equation x = A + Bt + Ct 2, where t represents time in seconds. What are the SI units of A, B, and C?
a. m, m, m
b. m, s, s2
c. m, s, s
d. m/s, m/s2, m/s3
e. m, m/s, m/s2 – correct
In uniform circular motion
the speed of the object is constant.
The centripetal force on an object in uniform circular motion
points toward the center of the circle.
If the speed of an object in uniform circular motion is doubled while the radius remains constant the centripetal force is multiplied by a factor of
4
If the radius in which an object moves in uniform circular motion is doubled while the speed remains constant the centripetal force is multiplied by a factor of
1/2
According to Kepler’s First Law, all planets have orbits about the Sun that are
ellipses.
According to Newton’s Law of Universal Gravitation, when the distance between the centers of two objects is tripled and the masses remain constant the force between the objects is multiplied by a factor of
1/9
If an artificial satellite is orbiting about the Earth between the Earth and the Moon, how does its period of rotation compare to the Moon’s period?
The satellite has a shorter period of rotation than the Moon.
Which is stronger, the Earth’s pull on the Moon, or the Moon’s pull on the Earth?
They are the same.
Work is defined as
the product of force and the distance through which the force acts.
If an equivalent amount of work is done in a shorter period of time
more power is required.
The fundamental unit of work and energy is the
Joule
If the velocity of an object is doubled its kinetic energy is multiplied by
4
If the height of an object above a reference level is doubled its gravitational potential energy is multiplied by
2
Kinetic energy is energy that an object possesses because of its
motion
if the distance a spring is stretched from its equilibrium position is doubled the elastic potential energy of the spring is multiplied by
4