Rotational kinematics on a plane

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SUMMARY

The discussion focuses on calculating the acceleration of the center of mass of a circular hoop rolling down a ramp inclined at 30 degrees. The correct acceleration is derived using the equation a = (1/2)g, where g represents gravitational acceleration. Participants emphasize the importance of applying both translational equations (F = ma) and rotational equations (τ = Iα) to solve the problem effectively. Additionally, the moment of inertia for the hoop and the relationship between angular acceleration and linear acceleration (α = a/r) are crucial for arriving at the solution.

PREREQUISITES
  • Understanding of rotational kinematics
  • Knowledge of Newton's second law (F = ma)
  • Familiarity with torque and moment of inertia concepts
  • Basic trigonometry, specifically sine functions
NEXT STEPS
  • Study the moment of inertia for different shapes, focusing on hoops and cylinders
  • Learn about the relationship between linear and angular motion in rolling objects
  • Explore the effects of friction on rolling motion and its role in torque
  • Practice solving similar problems involving inclined planes and rotational dynamics
USEFUL FOR

Students studying physics, particularly those focusing on mechanics, as well as educators looking for examples of rotational kinematics in practical applications.

dherm56
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Homework Statement



A circular hoop rolls down a ramp without slipping. The angle of the ramp with respect to horizontal is 30 degrees.


1) What is the acceleration of the center of mass of the hoop down the ramp?

a = ( 1/4 ) g
a = ( 1/3 ) g
a = ( 1/2 ) g
a = ( 2/3 ) g
a = ( 3/4 ) g

Homework Equations



rotational kinematics with potential and kinetic energy


The Attempt at a Solution



a=gsin30
a=.5g

I'm not sure if there is more to the problem, any suggestions
 
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dherm56 said:

Homework Statement



A circular hoop rolls down a ramp without slipping. The angle of the ramp with respect to horizontal is 30 degrees.


1) What is the acceleration of the center of mass of the hoop down the ramp?

a = ( 1/4 ) g
a = ( 1/3 ) g
a = ( 1/2 ) g
a = ( 2/3 ) g
a = ( 3/4 ) g

Homework Equations



rotational kinematics with potential and kinetic energy


The Attempt at a Solution



a=gsin30
a=.5g

I'm not sure if there is more to the problem, any suggestions

You should set up your coordinate system as usual (x axis along the plane; y-axis perpendicular). Then write a set of translational equations based on F = ma and a set of rotational equations based on

[tex]\tau = I \alpha[/tex]

You'll need the moment of inertia for the hoop and to recall that [tex]\alpha = \frac{a}{r}[/tex]. While you're considering the rotational motion, keep in mind that the force of friction caused the hoop to rotate. With all these pieces you should be able to arrive at the answer.
 
Write down the expression for net force and torque on sliding hoop and solve for a(cm)
 

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