# Vector Magnitude & Circular Motion – Physics

### 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

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?

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

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