# How long will it take for one cylinder to turn one revolution?

## Homework Statement

A cylinder is initially at rest, how long will it take for the cylinder to turn one revolution?

## Homework Equations

(Theta)f=(Theta)i+(alpha)(deltaT)

## The Attempt at a Solution

I know that the distance of the cylinder to turn one revolution is 2Pi over speed. My speed was 0.05 rad/s so i divided 2Pi/0.05 rad/s and it did not give me the right time which is 15.9 sec. Help?

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SammyS
Staff Emeritus
Homework Helper
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## Homework Statement

A cylinder is initially at rest, how long will it take for the cylinder to turn one revolution?

## Homework Equations

(Theta)f=(Theta)i+(alpha)(deltaT)

## The Attempt at a Solution

I know that the distance of the cylinder to turn one revolution is 2Pi over speed. My speed was 0.05 rad/s so i divided 2Pi/0.05 rad/s and it did not give me the right time which is 15.9 sec. Help?
Somehow, this problem, as stated, is rather incomplete.

If the cylinder is initially at rest, what makes it move at all? ... or what describes its subsequent motion?

ok sorry for not being specific.

this question is the second part of the firsst question which is this one.

A solid cylinder is pivoted about a frictionless axle as shown. A rope wrapped around the outer radius of 2 m exerts a downward force of 3N. A rope wrapped around the inner radius of 0.7 m exerts a force of 8 N to the right. The moment of inertia of the cylinder is 8 kg m^2. Find the angular acceleration.

I found the solution to this one by t=+-rFsin(theta) here is the specifics https://www.physicsforums.com/showthread.php?t=583881

However, my solution to the first part of the problem was the sum of all torque forces Sumt=I(alpha)

-Rfsin(theta)+rFsin(theta)=I(alpha) I had my Moment of inertia giving my the problem so all i had to do was to solve for (alpha) which gave me 0.05 rads/s.

The second part of the problem says,

If the cylinder in problem 10 is initially at rest, how long will it take for the cylinder to turn one revolution??

That is the part where i use (Theta)f=(Theta)i+(alpha)(deltaT) and solve for t but it did not give me the right answer.

SammyS
Staff Emeritus
Homework Helper
Gold Member
ok sorry for not being specific.

this question is the second part of the firsst question which is this one.

A solid cylinder is pivoted about a frictionless axle as shown. A rope wrapped around the outer radius of 2 m exerts a downward force of 3N. A rope wrapped around the inner radius of 0.7 m exerts a force of 8 N to the right. The moment of inertia of the cylinder is 8 kg m^2. Find the angular acceleration.

I found the solution to this one by t=+-rFsin(theta) here is the specifics https://www.physicsforums.com/showthread.php?t=583881

However, my solution to the first part of the problem was the sum of all torque forces Sumt=I(alpha)

-Rfsin(theta)+rFsin(theta)=I(alpha) I had my Moment of inertia giving my the problem so all i had to do was to solve for (alpha) which gave me 0.05 rads/s.

The second part of the problem says,

If the cylinder in problem 10 is initially at rest, how long will it take for the cylinder to turn one revolution??
Assuming that α is angular acceleration, it should have units of rad/s2 , not rad/s .

yes yes sorry for that one.

gneill
Mentor
That is the part where i use (Theta)f=(Theta)i+(alpha)(deltaT) and solve for t but it did not give me the right answer.
Angular kinematic equations have direct parallels to their linear counterparts. If θ is angular position, and ##\alpha## is angular acceleration, then your formula above is equivalent, in linear terms, to

## x_f = x_i + at ##

which is not correct. Appropriate linear formulas are:

##v_f = v_i + a t## and ##x_f = x_i + v_i t + (1/2)a t^2##.

and their angular counterparts:

##\omega_f = \omega_i + \alpha t## and ##\theta_f = \theta_i + \omega_i t + (1/2)\alpha t^2##.

hmm which one should I use because I dont have angular velocity I only have angular acceleration. How can i start up with?

gneill
Mentor
hmm which one should I use because I dont have angular velocity I only have angular acceleration. How can i start up with?
You drop any terms that are zero from the equations. For example, if ωi is zero, then ωit will always be zero.