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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

A solid, uniform disk of radius 0.250 m and mass 55.0 kg rolls down a ramp of length 4.50 m that makes an angle of 15.0° with the horizontal. The disk starts from rest from the top of the ramp. Find (a) the speed of the disk’s center of mass when it reaches the bottom of the ramp and (b) the angular speed of the disk at the bottom of the ramp.

(a)

To determine
The speed of the disk’s center of mass when it reaches the bottom of the ramp.

Explanation

Given info: The mass of the disk is 55.0kg , radius of the disk is 0.250m , length of the ramp is 4.50m , the angle of the ramp is 15° , and acceleration due to gravity is 9.80m/s2 .

Explanation:

The conservation of mechanical energy of the system is used for the speed of center of mass of the disk that is KEr,f+KEt,f+PEg,f=KEr,i+KEt,i+PEg,i but initially, the translational and rotational kinetic energies are zero. At the bottom of the slope, the potential energy would be zero. Now the conservation of mechanical energy is written as 12Iωf2+12mvt2+0=0+0+mglsinθ and the moment of inertia of the disk is I=mr2/2

(b)

To determine
The angular speed of the disk at the bottom of the ramp.

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