THS Math Trig FA24 Angular and Linear velocity

Front

What is the formula to calculate the central angle (θ) in radians given the arc length (s) and radius (r)?

Back

θ = s / r

Tags

CCSS.HSG.SRT.C.8

Front

How do you convert degrees to radians?

Back

Multiply degrees by π/180.

Tags

CCSS.HSF.TF.A.1

Front

What is the formula for the length of an arc (s) given the radius (r) and central angle (θ) in radians?

Back

s = r * θ

Tags

CCSS.HSG.C.B.5

Front

What is the formula for the area of a sector (A) given the radius (r) and central angle (θ) in radians?

Back

A = 0.5 * r^2 * θ

Tags

CCSS.HSG.C.B.5

Front

If a circle has a radius of 5 cm, what is the circumference (C) of the circle?

Back

C = 2 * π * r = 10π cm.

Tags

CCSS.7.G.B.4

Front

What is angular velocity (ω) and how is it calculated?

Back

Angular velocity (ω) is the rate of change of the angle with respect to time, calculated as ω = θ / t.

Front

How do you convert angular velocity from revolutions per minute (rpm) to radians per minute?

Back

Multiply rpm by 2π.

Tags

CCSS.HSF.TF.A.1

Front

What is the relationship between linear velocity (v), angular velocity (ω), and radius (r)?

Back

v = ω * r.

Front

If a wheel has a radius of 11 inches and rotates at 600 rpm, how do you find the linear speed in miles/hour?

Back

First, find ω in rad/min, then use v = ω * r and convert to miles/hour.

Front

What is the area of a sector with a central angle of 140° and radius of 8 cm?

Back

A = (140/360) * π * r^2 = 224π/9 cm² or ≈ 78.2 cm².

Tags

CCSS.HSG.C.B.5