Calculating Tire Rotation in Radians and Revolutions - Homework Problem Solution

  • Thread starter Thread starter sowmit
  • Start date Start date
Click For Summary
SUMMARY

The discussion focuses on calculating the angle in radians and the number of revolutions for a car tire with a diameter of 2.0 ft, warranted for 60,000 miles (3.2 x 109 ft). The correct formula to determine the angle of rotation is theta = s/r, where 's' is the distance traveled and 'r' is the radius of the tire. The correct calculation reveals that the angle of rotation is 3.2 x 108 radians, not 5.0 x 106 radians as initially calculated. Additionally, the discussion touches on finding the angular velocity (omega) in revolutions per second based on the tire's circumference.

PREREQUISITES
  • Understanding of basic geometry, specifically the relationship between diameter, radius, and circumference.
  • Familiarity with angular measurements, including radians and degrees.
  • Knowledge of linear motion equations, particularly the formula theta = s/r.
  • Basic concepts of angular velocity and its calculation.
NEXT STEPS
  • Study the relationship between linear distance and angular displacement in circular motion.
  • Learn how to calculate the circumference of a circle using the formula C = πd.
  • Research the concept of angular velocity and how to convert between radians and revolutions.
  • Explore practical applications of these calculations in automotive engineering and physics.
USEFUL FOR

This discussion is beneficial for students studying physics or engineering, particularly those focusing on mechanics and rotational motion. It is also useful for anyone involved in automotive design or maintenance who needs to understand tire dynamics.

sowmit
Messages
12
Reaction score
0
Please help me with this problem??

Homework Statement



The question is:

the tires on a new car have a diameter of 2.0 ft and are warranted for 60000 miles (3.2*e^9 ft).

(a) Determine the angle (in radians) through which one of the tires will rotate?

(b) How many revolutions are equivalent to ur answer in part a?>

Homework Equations


theta = s/r


The Attempt at a Solution



theta = (3.2*e^9 ft / 1.0 ft) * (2pi radian/ 360 degree) = 5.0* 10^6 radian, but the answer says 3.2*e^8 radians. How's that possible.

How do I find omega (revolution per second?)
 
Physics news on Phys.org


When the wheel has moved forward by one circumference, it has rotated by 2π radians.
How many circumferences can fit in 60,000 miles?

Why do you want to find omega?
 

Similar threads

Revolutions of a tire and angle in radians thru warranty
  • · Replies 3 ·
Replies
3
Views
2K
Car Tire Wear and Odometer Accuracy Calculation
  • · Replies 4 ·
Replies
4
Views
3K
How to calculate angular speed?
  • · Replies 7 ·
Replies
7
Views
3K
Rotational motion problems involving radians
  • · Replies 1 ·
Replies
1
Views
2K
How Do You Calculate the Angular Motion of a Pulley System?
  • · Replies 15 ·
Replies
15
Views
2K
Time for Revolution (Rotating about the Center of Mass)
  • · Replies 4 ·
Replies
4
Views
1K
MHB Determining Miles Traveled From Tire Diameter and Rotations.
  • · Replies 6 ·
Replies
6
Views
2K
Centripetal Acceleration Problem: Finding Angular Speed
  • · Replies 2 ·
Replies
2
Views
2K
Calculating the Radius of a Rotating Wheel Using Radians and Arc Length
  • · Replies 2 ·
Replies
2
Views
2K
How Far Does a Hamster Run in Its Wheel in One Night?
  • · Replies 5 ·
Replies
5
Views
3K