Arc Length and Angular Speed

What radians were actually invented for.

12 problems · about 21 minutes · F-TF.A.1, G-C.B.5

NameDate

Figure — use these to answer the problems

Change the radius and watch the circumference follow. A full turn is 2π radians of arc.

Radius4

Figure 1

Straightforward practice. Get the method working first.

5 problems

Radius 7, angle 2 radians. What is the arc length?
Answer
2
Why must θ be in radians for s = rθ?
- A radian is defined as one radius of arc, so the formula needs no extra factor.
- Radians are simply easier to type.
Radius 8, angle 2 radians. Arc length?
Answer
Radius 4, angle 3 radians. Sector area?
Answer
Arc 20, radius 5. What is the angle in radians?
Answer

The same ideas with more to keep track of.

3 problems

Radius 3 m, angular speed 5 rad/s. Linear speed in m/s?
Answer
How many radians is one full turn, to two decimal places?
Answer
A wheel turns 10 times per second. Angular speed in radians per second, to one decimal place?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

9
Two points sit on the same spinning wheel, one near the hub and one at the rim. Which statements are true?
- They share the same angular speed.
- The rim point has the greater linear speed.
- They share the same linear speed.
- The hub point has the greater angular speed.
- Tick every box that applies.
Sector area 50, radius 10. Angle in radians?
Answer
The Arc
Radius 5, angle 3 radians. What is the arc length?
Answer
The Wheel
A wheel of radius 0.5 m spins at 4 radians per second. What is the rim speed, in metres per second?
Answerm/s