ROTATION: A solid ball of mass 2.6 kg and diameter 15cm is rotating about its axis at 80 rev/min. A. What is its kinetic energy? Answer in units of mJ B. If an additional 1 J of energy are supplied to the rotational energy, what is the new angular speed of the ball? Answer in units of rev/min  

Expert Answers

An illustration of the letter 'A' in a speech bubbles

This needs the basic understanding of rotational dynamics.

Kinetic energy of a rotating mass is

KE = (I * w^2)/2

where I is the moment of inertia and w (omega) is the rotational velocity in radians per second

Now for a sphere with uniform density rotating around its axis I is,

I = (2MR^2)/5

M -mass, R -Radius

For this case,

 

I = (2x2.6kgx(0.15m)^2)/5 = 0.0234 kgm^2

 

w = 80 rpm = (80 x 2xpi)/60 radians per second

w = 8.3776 rads^-1

Therefore the kinetic energy is KE

KE = 0.5 x 0.0234 kgm^2 x 8.3776^2 s-2

KE = 0.82115 J = 821.15 mJ

 

If additonal 1Jof kinetic enrgy is inserted, the new kinetic enrgy is 1.82115 J

Since moment of inertia doesnt change, KE is directly proportionate to w^2

 

therefore,

(1.82115/0.82115) = (w^2)/(80^2)

w^2 = 14193.94751

w = 119.138 rev per min

(I used rev per min instead of rads^-1, because the units cancel out)

 

 

 

 

 

 

 

Approved by eNotes Editorial Team

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial