Question

(b) A wheel of radius 5 in. is rotating 45°/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec?

Answer 1

\[v=r \omega \] This is the formula to go from translational velocity to angular velocity

Answer 2

\[\frac{ 45rev }{ 1\sec }*\frac{ 60\sec }{ 1\min }=2700 rev/min\]

Answer 3

That was the angular speed

Answer 4

1 revolution = 2pi
\[2700\frac{ rev }{ \min }*\frac{ 2\pi rads }{ 1rev }=5400\pi \frac{ rads }{ \min }\]

Answer 5

Its 45 degrees per second do you just assume that it is a rev

Answer 6

Oh sorry. I didn't notice that

Answer 7

change degrees to radians

Answer 8

45 degrees= pi/4 radians btw

Answer 9

Of so then what does that do for the rev/min

Answer 10

\[\frac{ 45^{o} }{ 1\sec }*\frac{ 1rev }{ 360^{o} }=\frac{ 1rev }{ 8\sec }\]

Answer 11

\[\frac{ 1rev }{ 8\sec }*\frac{ 60\sec }{ 1\min }=7.5\frac{ rev }{ \min }\]