Advanced Math

Review 4A-0 to 4A-1b

Angles, Radians, Velocity

Angles, Radians, Velocity

Change 5π/3 rad to degrees

Angles, Radians, Velocity

300°

Angles, Radians, Velocity

Change 55°10’20” to decimal degrees.

Angles, Radians, Velocity

≈ 55.172°

Angles, Radians, Velocity

Change 28.254° to degrees,

minutes, and seconds.

Angles, Radians, Velocity

28°15’14.4”

Angles, Radians, Velocity

What is a radian?

Angles, Radians, Velocity

An angle measure such that the arc

struck off by a central angle is equal in

length to the radius of the circle.

Angles, Radians, Velocity

How many radians in one revolution?

Angles, Radians, Velocity

2π

Angles, Radians, Velocity

Define velocity

Angles, Radians, Velocity

Distance per time unit. Linear velocity is a linear

distance (mi., cm, m., ft., etc.) divided by some

time unit. Angular velocity is an angle measure

(rad., rev., °) divided by some time unit.

Angles, Radians, Velocity

Here is a summary of formulas and

important conversion factors.

rωt

rθ

t

sV ,

t

θω θ,r

2

1A

rθs rad, 2πrev 1 ,180rad π

2

S

Angles, Radians, Velocity

Change 2 rpm to radians per second.

Angles, Radians, Velocity

π/15 ≈ 0.21 rad/s

Angles, Radians, Velocity

A gear makes 1.5 revolutions every 2

seconds. Find the angular velocity of a

point on the gear in radians per second.

Angles, Radians, Velocity

1.5π ≈ 4.7 rad/s

Angles, Radians, Velocity

Determine the linear velocity of a point on

a circle 1.4 m from the center that moves

through 450° in 1 minute. Express the

answer in cm/s and in terms of π.

Angles, Radians, Velocity

35π/6 ≈ 18.3 cm/s

Angles, Radians, Velocity

A car traveling at 100 kph has a wheel

radius of 30 cm. Find the rpm of the wheel.

Angles, Radians, Velocity

≈ 884 rpm