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Rolling ball down slope at specific time

  • #1

Homework Statement


A uniform solid ball rolls down a slope. If the ball has a diameter of .5m and a mass of .1 kg find the following:

The equation which describes the velocity of the ball at any time, given that it starts from rest.


Homework Equations



I've tried using energy equations, thus: 1/2 Iw^2+1/2Mv^2+mgh = constant (Kf +Uf = Ki + Ui) but that doesn't have "t" as a variable. I have also tried θ-θi=1/2(ωi+ω)t. But that didn't end up taking the radius or mass into consideration.

The Attempt at a Solution



More or less stated in the relevant equations. This is due in a few hours, so anything is much appreciated. Thank you in advance!
 

Answers and Replies

  • #2
rl.bhat
Homework Helper
4,433
7
Moment of inertia of the sphere is 2MR^2/5 and v = R*w.
So the rotational kinetic energy is given by 1/2*I*w^2 = 1/2*2M*R^2/5*v^2/R^2 = M*v^2/5.
And h = 1/2*g*sin(theta)*t^2.
Substitute these values in the relevant equation to solve for t.
 

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