Rotational Inertia Hill Problem

Click For Summary
SUMMARY

The discussion focuses on calculating the linear speed of a bicycle wheel rolling down an 8-meter hill, starting with an initial speed of 0.5 m/s. The relevant equations include the moment of inertia \(I = \frac{1}{2}mr^2\) and the conservation of energy principle, which states that the sum of kinetic energy (KE) and potential energy (PE) remains constant. Participants emphasize the need to incorporate both linear and rotational kinetic energy in the calculations to find the final linear speed at the bottom of the hill.

PREREQUISITES
  • Understanding of rotational inertia and its formula \(I = \frac{1}{2}mr^2\)
  • Knowledge of conservation of energy principles in physics
  • Familiarity with kinetic energy equations, including linear and rotational components
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study the conservation of mechanical energy in rolling motion
  • Learn how to derive the final linear speed from potential energy and kinetic energy equations
  • Explore the relationship between linear speed and rotational speed in rolling objects
  • Investigate the effects of initial conditions on the final speed of rolling objects
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the dynamics of rolling motion and energy conservation principles in mechanics.

cnfsdstudent
Messages
5
Reaction score
0
A bicycle wheel is rolled down a hill that is 8 m high, Determine the linear speed of the wheel at the bottom of the hill if the wheel is moving initially at .5 m/s


I= 1/2mr^2

mgh=1/2mv^2



I know it is set up like a KE equation, and I also know I am missing a variable to solve for on the mgh side. Does anyone know what that variable might be? I know it isn't torque.
 
Physics news on Phys.org
Welcome to PF!

Hi cnfsdstudent! Welcome to PF! :smile:

(try using the X2 tag just above the Reply box :wink:)

You need KE + PE = constant, and also KE = linear KE + rotational KE. :smile:
 

Similar threads

Oscillatory motion problem: Bicycle wheel rotation oscillation
  • · Replies 17 ·
Replies
17
Views
1K
Parallel Axis Theorem Not Working
  • · Replies 28 ·
Replies
28
Views
2K
Rotational Inertia: Hoop vs Disk
  • · Replies 19 ·
Replies
19
Views
5K
Force on a rotating wheel/disc
  • · Replies 25 ·
Replies
25
Views
2K
A cylinder of snow rolls down a hill gathering more snow -- calculate its speed
  • · Replies 39 ·
2
Replies
39
Views
4K
Angular momentum and rotational inertia
  • · Replies 25 ·
Replies
25
Views
3K
Have a problem with this Rotational Motion question
  • · Replies 5 ·
Replies
5
Views
2K
Energy calculations for a skier on a hill
  • · Replies 6 ·
Replies
6
Views
6K
How Does the Rotational Inertia Affect Rolling Motion on an Inclined Plane?
  • · Replies 3 ·
Replies
3
Views
3K
Correct Use of the Parallel Axis Theorem for Moment of Inertia
  • · Replies 2 ·
Replies
2
Views
2K