Free help with homework

Why join Brainly?

  • ask questions about your assignment
  • get answers with explanations
  • find similar questions

A ball of radius r rolls inside a heavy spherical shell of radius R.It is released from rest from point A.What is the angular velocity of the centre of the

ball in position B about the center of shell



This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
See the diagram. 
Initial position  A and final position B.

OC = (R - r) Sin α
OD = (R - r) Sin (α+ Ф)
CD = h = (R -r) 2 SinФ/2 Cos(α+Ф/2)

moment of inertia of the ball about diameter = 2/5 * m r²
v = r ω

we apply the law of conservation of energy.

m g h = 1/2 m v² + 1/2 I ω²
=> 2 g h =  r² ω² + 1/5 * r² ω²
     ω² = (5/3) g h / r²
     ω = √ [10 g (R - r) SinФ/2 Cos (α+Ф/2) / r²]

If  α = 0, then    ω = (1/r) * √ [ 5 g (R - r) SinФ ]

1 5 1
click on thanks button above pls; ;; select best answer
The Brain
  • The Brain
  • Helper
Not sure about the answer?
Learn more with Brainly!
Having trouble with your homework?
Get free help!
  • 80% of questions are answered in under 10 minutes
  • Answers come with explanations, so that you can learn
  • Answer quality is ensured by our experts