A wheel passes 600 pi cm for 10 rotations. What is the radius of the wheel?
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Radius r=1.5m,α=10rad/s
2
initial angular speed w
0
=
π
60
rpm
=2π×
π
60
×
60
1
rad/s
=2rad/s
Time t=2s
From rotational kinematics
w=w
0
+αt
2+10×2
=2+20
=22rad/s
and θ=w
0
t+
2
1
αt
2
=2×2+
2
1
×10×4
=4+20
=24rad
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We illustrate the precession of a gyroscope with an example of a top in the next two figures. If the top is placed on a flat surface near the surface of Earth at an angle to the vertical and is not spinning, it will fall over, due to the force of gravity producing a torque acting on its center of mass
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