A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere. The tip of the axle is placed on a support. What is the top’s precession frequency in rpm?
The precession frequency of the top is .
The mass of the spherical top is
The radius of the spherical top is
Spin angular velocity is
Convert spin angular velocity from to .
The moment of inertia of the solid spherical top is .
The precession frequency is given by .
From the above two equations
Substitute the given values
The precession frequency in rpm is
Therefore, the precession frequency of the top is .
Blocks of mass m1 and m2 are connected by a massless string that passes over the pulley in Figure P12.65. The pulley turns on frictionless bearings. Mass m1 slides on a horizontal, frictionless surface. Mass m2 is released while the blocks are at rest. a. Assume the pulley is massless. Find the acceleration of m1 and the tension in the string. This is a Chapter 7 review problem.b. Suppose the pulley has mass mp and radius R. Find the acceleration of m1 and the tensions in the upper and lower portions of the string. Verify that your answers agree with part a if you set mp = 0.
Consider a solid cone of radius R, height H, and mass M. The volume of a cone is 1/3 πHR2
a. What is the distance from the apex (the point) to the center of mass? b. What is the moment of inertia for rotation about the axis of the cone? Hint: The moment of inertia can be calculated as the sum of the moments of inertia of lots of small pieces.
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