Trig 3.4 Linear and Angular Speed

Front

What is Linear Speed?

Back

Linear Speed is the distance traveled per unit of time, typically measured in units like miles per hour (mph).

Front

What is Angular Speed?

Back

Angular Speed is the rate of rotation, measured in radians per second or degrees per second.

Front

How do you convert revolutions per minute (rpm) to radians per hour?

Back

Multiply the rpm by 2π to convert to radians per minute, then multiply by 60 to convert to radians per hour.

Tags

CCSS.HSF.TF.A.1

Front

What is the formula for calculating Angular Speed?

Back

Angular Speed (ω) = θ / t, where θ is the angular displacement in radians and t is the time in seconds.

Front

What is the relationship between Linear Speed and Angular Speed?

Back

Linear Speed (v) = Angular Speed (ω) × Radius (r).

Front

If a wheel makes 10 revolutions in 1 minute, what is its Angular Speed in radians per second?

Back

Angular Speed = 10 rev/min × (2π rad/rev) × (1 min/60 sec) = π/3 rad/sec.

Front

What is the unit of Angular Distance?

Back

The unit of Angular Distance is radians.

Tags

CCSS.4.MD.C.6

Front

How do you calculate the Linear Distance traveled by a point on a rotating object?

Back

Linear Distance = Angular Distance (in radians) × Radius.

Tags

CCSS.HSG.SRT.C.8

Front

What is the Angular Speed of a ceiling fan that makes 45 revolutions per minute?

Back

Angular Speed = 45 rev/min × (2π rad/rev) = 90π rad/min or 5400π rad/hr.

Front

What is the Angular Speed of a car tire with a diameter of 14 inches spinning at 10 revolutions per second?

Back

Angular Speed = 10 rev/sec × (2π rad/rev) × (3600 sec/hr) = 72000π rad/hr.