Solve Basic Torque Problem: Find Downward Accel with Mass m & Radius r

[oreosama]

Homework Statement

a hoop of mass m and radius r has a cord wrapped around it the hoop is released while holding the string the hoop rolls without slippage
write out force and torque eqns on the hoop
given m, r determine downward accel

Homework Equations

Torque = I alpha
Torque = r x F

The Attempt at a Solution

Torque = I * alpha
I of hoop = m*r^2
alpha = r*a

r x F = m*r^3 * a


this F must have relationship to gravity and tension right? if it were ma then my as cancel

Fy should be ma = Tension - mg ?

im lost at this point, thanks for any help

 

[SammyS]

Homework Statement

a hoop of mass m and radius r has a cord wrapped around it the hoop is released while holding the string the hoop rolls without slippage
write out force and torque eqns on the hoop
given m, r determine downward accel

Homework Equations

Torque = I alpha
Torque = r x F

The Attempt at a Solution

Torque = I * alpha
I of hoop = m*r^2
alpha = r*a

r x F = m*r^3 * a

this F must have relationship to gravity and tension right? if it were ma then my as cancel

Fy should be ma = Tension - mg ?

im lost at this point, thanks for any help

Draw a free body diagram for the hoop.

Torque is calculated about some reference point. What point are you choosing?

The following link includes the excerpt below: https://www.physicsforums.com/showthread.php?t=414380

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