8.09 Linear and angular speed
Interactive practice questions
Consider the following diagram, in which point $P$P is rotating counterclockwise around the unit circle at a constant velocity.
Fill in the blank: The measure of how fast the position of point $P$P is changing is the ___________.
Angular speed (or velocity)
Linear speed (or velocity)
Quadratic speed (or velocity)
Circular speed (or velocity)
Fill in the blank: The measure of how fast the angle $\theta$θ is changing is the ______.
Angular speed (or velocity)
Circular speed (or velocity)
Linear speed (or velocity)
Spiral speed (or velocity)
If the angular speed of point $P$P is $\frac{\pi}{4}$π4 radians/sec, what is the linear speed of point $P$P?
If $P$P is rotating with an angular speed of $\frac{\pi}{2}$π2 radians/sec, how far will $P$P travel in $20$20 seconds?
If the angular speed $\omega=\frac{\pi}{5}$ω=π5 radians per second and the rotation time $t=8$t=8 seconds, find the rotation angle $\theta$θ.
An object moves along the edge of a circular disk at $\omega=\frac{5\pi}{6}$ω=5π6 radians per second. The disk has a radius $r=9$r=9 yards.
Find the distance $s$s along the edge of the disk that the object will travel in $t=8$t=8 seconds.
Tobias is riding a motorbike with wheels that have a diametre of $80$80cm and that are rotating at $42$42 radians per second.