Is This Physics Calculation Correct for a Decelerating Rotating Ball?

[dman_PL]

Homework Statement

Can someone check if this is right? The time seems okay, but the work I feel is wrong

A ball with moment of inertia 0.1kg · m2 is rotating on a table, but
friction is slowing it down with constant angular acceleration. The ball is originally spinning at 2π radians per second, but slows down to 10 percent of that value in 2 seconds


1) How long does it take the ball to come to rest (time since it began spinning)
2)How much work is done on the ball to bring it to rest

Homework Equations

1)Since angular acceleration is constant, we use ∆ω = α∆t
2)W = ∆K = Kf − Ki = 0 −1/2Iω

The Attempt at a Solution

1) Since I have the ball spinning at 2π/sec, and it slows down -10% of the original speed in two seconds, so i plug in the information into the equation. so Δw= (-.10)(2π)/2sec which equals -.314159. Which then I can solve for t. New equation: t=Δw/α. So -.314159/-.628318= 5 Sec.
2) (-1/2)(.1kg*m^2)(.628318)^2=-.0197J

 

[Andrew Mason]

Homework Statement

Can someone check if this is right? The time seems okay, but the work I feel is wrong

A ball with moment of inertia 0.1kg · m2 is rotating on a table, but
friction is slowing it down with constant angular acceleration. The ball is originally spinning at 2π radians per second, but slows down to 10 percent of that value in 2 seconds1) How long does it take the ball to come to rest (time since it began spinning)
2)How much work is done on the ball to bring it to rest

Homework Equations

1)Since angular acceleration is constant, we use ∆ω = α∆t
2)W = ∆K = Kf − Ki = 0 −1/2Iω

Check this. The rotational kinetic energy has dimensions of kg m^2/sec^2. This has dimension of kg m^2/sec.

The Attempt at a Solution

1) Since I have the ball spinning at 2π/sec, and it slows down -10% of the original speed in two seconds, so i plug in the information into the equation. so Δw= (-.10)(2π)/2sec which equals -.314159. Which then I can solve for t. New equation: t=Δw/α. So -.314159/-.628318= 5 Sec.
2) (-1/2)(.1kg*m^2)(.628318)^2=-.0197J

Better to find the algebraic solution and then plug in numbers.

First, find the angular deceleration α. Then use that to find the time it takes to stop using the correct expression for rotational energy.

AM

 

[dman_PL]

Check this. The rotational kinetic energy has dimensions of kg m^2/sec^2. This has dimension of kg m^2/sec.
Better to find the algebraic solution and then plug in numbers.

First, find the angular deceleration α. Then use that to find the time it takes to stop using the correct expression for rotational energy.

AM

So to find α, I am still using Δω/Δt correct?

 

[Andrew Mason]

So to find α, I am still using Δω/Δt correct?

Correct. You don't have to use energy to work out the time it takes to stop. Just use α = Δω/Δt. What is the change in ω when it stops? Knowing α and Δω you can work out the Δt.

AM

 

[asteriatic]

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Your solution for part 1 seems correct. However, for part 2, the work done should be a positive value, since work is the product of force and displacement in the direction of the force. In this case, the work done is to slow down the spinning ball, so the force would be in the opposite direction of the displacement. Therefore, the correct equation for work would be W = -∆K = -Kf + Ki = -1/2I(ωf^2 - ωi^2) = -1/2(0.1)(0 - (2π)^2) = 1.57 J. This means that 1.57 J of work is done on the ball to bring it to rest.