Determine the angular velocity of the Wheel

Click For Summary
SUMMARY

The discussion focuses on determining the angular velocity of a wheel given a cart velocity of 3.4 ft/sec. The user initially calculated the angular speed using the equation vA = vO + vA/O, resulting in an angular velocity of 5.597 revolutions per minute (rev/min). However, the user later identified an error in their calculations due to not converting the radius from inches to feet. The correct angular velocity is derived from the formula w = v/r, where v is the linear velocity and r is the radius in consistent units.

PREREQUISITES
  • Understanding of angular velocity and linear velocity concepts
  • Familiarity with vector addition in physics
  • Knowledge of unit conversion (inches to feet)
  • Proficiency in using the equation w = v/r for rotational motion
NEXT STEPS
  • Review the principles of rotational dynamics and angular motion
  • Practice unit conversion techniques, especially between inches and feet
  • Explore vector addition and its application in physics problems
  • Learn about the relationship between linear and angular velocity in different contexts
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and rotational motion, as well as educators looking for examples of angular velocity calculations.

Northbysouth
Messages
241
Reaction score
2

Homework Statement


The cart has a velocity vc = 3.4 ft/sec to the right. Determine the angular speed N (positive if counterclockwise, negative if clockwise) of the wheel so that point A on the top of the rim has a velocity (a) equal to 3.4 ft/sec to the left, (b) equal to zero, and (c) equal to 6.8 ft/sec to the right.

I have attached an image of the question


Homework Equations





The Attempt at a Solution



vA = vO + vA/O

vO = -3.4i

v = wXr

r = 11.6j

For part a)

-3.4i = 3.4i + wX<11.6j>

Solving for w gives me

w = 6.8/11.6 k rad/sec

Which is equivalent to

w = 5.597 rev/min

I don't think this is right and I can't see what's wrong with what I've done.

Advice would be greatly appreciated.
 

Attachments

  • dyn 5.060.png
    dyn 5.060.png
    18 KB · Views: 857
Physics news on Phys.org
Nevermind, I found my mistake. I forgot to convert the 11.6" to feet.
 

Similar threads

What is the final angular velocity of each cylinder
  • · Replies 1 ·
Replies
1
Views
2K
How Far Does a Hamster Run in Its Wheel in One Night?
  • · Replies 5 ·
Replies
5
Views
3K
Angular Velocity of a wheel problem
  • · Replies 4 ·
Replies
4
Views
3K
Rolling Wheel / quick question -- Linear and Angular Velocity
  • · Replies 2 ·
Replies
2
Views
2K
Angular Acceleration Homework: 962 Revolutions in 10 Secs
  • · Replies 1 ·
Replies
1
Views
4K
Finding angular speed by conservation of angular momentum
  • · Replies 7 ·
Replies
7
Views
2K
Calculating Flywheel Rotations in Angular Speed and Constant Acceleration
  • · Replies 10 ·
Replies
10
Views
2K
Need help calculating angular velocity
  • · Replies 13 ·
Replies
13
Views
2K
Angular Velocity and Acceleration
  • · Replies 3 ·
Replies
3
Views
2K
Calculating Angular Velocity and Tensions After a Ball Hits a Board at an Angle
  • · Replies 6 ·
Replies
6
Views
2K