Calculate Linear Velocity: 180 deg/s & 0.5 m

[PepperABLF12]

Homework Statement

What is the linear velocity of the foot if the angular velocity of the dynamometer was 180 degrees/s and the distance from the knee joint to the foot is 0.5 m. Give your answer rounded to two decimal places in m.s-1. (Do not include units in answer).

Homework Equations

linear velocity = angular velocity (w) x radius (r).
linear velocity = w x r.

The Attempt at a Solution

w = 180 degree/s
r = 0.5m
linear velocity = ?

linear velocity = w x r
linear velocity = 180 x 0.5
linear velocity = 90 degrees/s

To find radians, 90/57.3 = 1.57 m/s

Is this correct? And in the right units?

Please help and thank you! :)

 

[BvU]

Well, your relevant equation gives $0.5 {\rm m}\, \times \,\pi \, {\rm rad/s} = 1.57 \,{\rm m/s}$ straightforward.

But your dealing with units is a bit messy. Especially the 90 degrees/s is objectionable. A linear velocity has dimension length/time. The numerics are fine, but the dimensions should read something like: degrees/s / radians/degree x meters/radian

THe writer of the exercise doesn't want to be bothered by these considerations, so he/she asks for a number only.

In my first sentence I let the radians disappear, you could say that I cheat too. My defence is: radians is arc per radius, so length/length and thereby dimensionless: it can be skipped in dimensional expressions.

 

[PepperABLF12]

Thank you so much! Great help :)

 

[dauto]

It is easier to understand if you convert to radians first and then calculate the linear velocity.

 

[HalfLostAndSearching]

Yes, your calculation is correct. However, the units for linear velocity should be in meters per second (m/s) instead of radians per second (rad/s). Therefore, the final answer should be 1.57 m/s. Keep in mind that radians and degrees are two different units for measuring angles, so it is important to use the correct unit when converting between them.