Radius of disk suspended on its edge

[songoku]

Homework Statement

A disk is suspended by a nail such that the pivot in a vertical plane about a point on the edge of the disk. If the period of oscillation of the disk is 1.25 s, what is the disk's radius?
a. 26 cm
b. 78 cm
c. 51 cm
d. impossible to know without the disk's mass

Relevant Equations

ω = 2π / T

I can calculate the angular speed but I don't know how to calculate the radius. Is there certain formula to calculate it?

Thanks

 

[andrewkirk]

The trick will be to convert this into a problem involving a simple pendulum. Then you can use the formulas for motion of a pendulum.

To do that, first find the moment of inertia (MOI) of the disk around the pivot, which will be a function of the radius R and the density ρ of the disk (kg per sq metre of surface area). To find that, find the MOI of the disk around its centre (Wikipeda has a list of moments of inertia, including that of a disk), then use the Parallel Axis Theorem.

Next, convert it to a problem involving a point mass on the end of a string - the classic simple pendulum problem. To do that, work out the distance L from the pivot that a point mass has to be in order to have the same MOI about the pivot as the disk does. That will give you r in terms of R, as ρ will cancel out.

Then plug the given oscillation period into the standard formula for period of a simple pendulum to calculate L, and calculate R from that.

 

[ehild]

Homework Statement: A disk is suspended by a nail such that the pivot in a vertical plane about a point on the edge of the disk. If the period of oscillation of the disk is 1.25 s, what is the disk's radius?
a. 26 cm
b. 78 cm
c. 51 cm
d. impossible to know without the disk's mass
Homework Equations: ω = 2π / T

I can calculate the angular speed but I don't know how to calculate the radius. Is there certain formula to calculate it?

Thanks

Show how did you calculate the angular speed?
It is a "Physical Pendulum", Browse or read http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

 

[songoku]

The trick will be to convert this into a problem involving a simple pendulum. Then you can use the formulas for motion of a pendulum.

To do that, first find the moment of inertia (MOI) of the disk around the pivot, which will be a function of the radius R and the density ρ of the disk (kg per sq metre of surface area). To find that, find the MOI of the disk around its centre (Wikipeda has a list of moments of inertia, including that of a disk), then use the Parallel Axis Theorem.

Next, convert it to a problem involving a point mass on the end of a string - the classic simple pendulum problem. To do that, work out the distance L from the pivot that a point mass has to be in order to have the same MOI about the pivot as the disk does. That will give you r in terms of R, as ρ will cancel out.

Then plug the given oscillation period into the standard formula for period of a simple pendulum to calculate L, and calculate R from that.

Show how did you calculate the angular speed?
It is a "Physical Pendulum", Browse or read http://hyperphysics.phy-astr.gsu.edu/hbase/pendp.html

I think I get the hint.

Thank you very much andrewkirk and ehild