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Unformatted text preview: Because th
(b) the frictional force acting onnormal and
assumed to incline for which the ball will roll without slipping.
(c) the maximum angle of the be acting at the center of mass, and the normal force
center of mass, the only force which exerts a torque about the c
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the frictional force. Let the mass of the basketball be m and app
Solution
law to find a system of simultaneous equations that we can solve f
(a) We can begin by writing down problem statement.
called for in the Newton’s y laws for the ball, including the torques: Fx = −mg sin θ + Ff = −ma
Fy = −mg cos θ + Fn =
0
τi =
Ff R
= Iα.
Furthermore, since the ball is rolling without slipping, we have that a = αR. So, we
have enough to solve this system of equations. Plugging in Ff = Iα/R = Ia/R2 to
the ﬁrst equation and solving for a gives
a= r
Fn m
x r
0 r
f r
mg θ mg sin θ
.
m + I/R2
nd ∑
∑F ( of inertia of the spherical law in I = 2
The momenta) Apply Newton’s 2shell is just both mR2 , and soFx
3
translational and mg sin θ
rotational form to
3
= g sin θ.
a=
2
m + 2m/3R
5
the ball...
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This document was uploaded on 03/14/2014 for the course PHYS 18 at UC Merced.
 Spring '10
 collins
 Physics, Work

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