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Angular Speed and Linear Speed problems

Converting between Angular Speed and Linear Speed example question

The angular speed ω of a point moving in a circle is defined as the quotient θ/t, where θ is the angle in radians through which the point travels in time t.

a) Find the angular speed of a point that moves through an angle of 4 radians in 6 seconds

b) Find the angular speed of a point on the rim of a wheel that travels at 60 rpm (revolutions per minute)

c) Show that the linear speed v of a point moving in a circle is related to the angular speed by the formula v = rω

d) A car is moving at the rate of 60 miles per hour, and the diameter of each wheel is 2.5 feet. Find the angular speed of the wheels.

 

Solution to this Angular Speed Linear Speed practice problem is provided in the video below!



 

Two Column Geometry Proof problems

Two Column Geometry Proof Intersecting Lines example problem

Given: GA = RA, AH = AT

Prove: GT is congruent to RH

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Trapezoid example

Given: AD = 8, BC = 8, and BC is congruent to CD

Prove: AD is congruent to CD

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Circle example question

Given:  is a diameter

Prove: (CD)2 = (AD)(DB)

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example problem

Given:

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example #2

Given: with the bisector of

Prove: BFDE is a rhombus

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Circle example question #2

Given: Circle with center O and diameter  

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Kite example problem

Given: Kite ABCD with

E, F, G, H are midpoints of

Prove: EFGH is a rectangle

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example #3

Given: bisects

is a perpendicular bisector of

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Triangle example question #4

Given:  is isosceles and  

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!



Two Column Geometry Proof Parallel Lines Transversal Triangle example problem

 

Given:

bisects  

bisects

Prove:

 

Solution to this Two Column Geometric Proof practice problem is given in the video below!






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