Phys223

Rolling Motion

Derive an equation for the moment of inertia using

translational and rotational

dynamics

and

kinematics

.

Draw

an

extended FBD

for

the hoop.

Include coord system

and label

all quantities

Use your FBDs to set up your dynamics

equations. Don’t solve here:

x

F

y

F

In the last equation, indicate with subscripts whether you are considering the torques (and

moment of inertia) about the center of mass or the

point of contact between the hoop and the

track.

List the acceleration constraint (how are

and a

cm

related?):

r

1

r

2

Phys223

Rolling Motion

Use kinematics to express the acceleration a

cm

in terms of quantities you measured (i.e. in terms

of time t, track length d, and angle of incl

ine

. If you measured height h instead of

, express h

in terms of

.

Solve your equations for the moment of inertia about the center of mass. Call this quantity I

M2

.

Note: you should only have measured qu

antities on the right hand side.

Final answer: I

M2

=

Phys223

Rolling Motion

d

h

Derive an equation for the moment of inertia using

conservation of energy and

kinematics

.

Use kinematics to find the final speed v of the hoop:

Set up the equation for conservation of energy:

From the

above equation, eliminate the angular velocity (express it in terms of v). Then solve

the equation for the moment of inertia. Make sure the right hand side has only measured

quantities in it:

Final answer:

## Comments 0

Log in to post a comment