1 / 7

Angular to Linear Movements

Angular to Linear Movements. Linear velocity (v) can be determined using angular velocity ( w ) and arclength (s) calculations. There are two methods: Calculate the angular velocity in rad/sec and multiply by the radius OR Calculate the arclength and divide by time.  q. r.

raymond-hernandez
Télécharger la présentation

Angular to Linear Movements

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Angular to Linear Movements Linear velocity (v) can be determined using angular velocity (w) and arclength (s) calculations. There are two methods: Calculate the angular velocity in rad/sec and multiply by the radius OR Calculate the arclength and divide by time

  2. q r General Example Basic Situation An object moves through a circular path with a radius r. The angle through which it moves is q0, and it makes this movement over time interval t. Calculate the linear velocity of the object.

  3. Angular to Linear Velocity Solution • Calculate the angular velocity • = q/t deg/sec • Convert w from deg/sec to rad/sec (w deg/sec)(1 rad /57.3 deg) = w rad/sec • Multiply angular velocity in rad/sec by the radius of the curve (w rad/sec)(r) = v

  4. ArclengthSolution • Convert the angle from deg to rad (q0)(1 rad/57.3 deg) = q rad • Calculate the arclength (s) s = (r)(q rad) • Divide the arclength by the time interval s/t = v

  5. q r EXAMPLE q = 800 r = 10 cm t = 5 sec

  6. Angular to Linear Velocity Solution • w = 80 deg/5 sec = 16 deg/sec • (16 deg/sec)(1 rad/57.3 deg) = .279 rad/sec • v = (.279 rad/sec)(10 cm) = 2.79 cm/sec

  7. Arclength Solution • (80 deg)(1 rad/57.3 deg) = 1.396 rad • s = (1.396 rad)(10 cm) = 13.96 cm • v = (13.96 cm)/(5 sec) = 2.79 cm/sec

More Related