Question

the diameter of the base of a tapered drinking cup is 5.0 cm. The diameter of...

the diameter of the base of a tapered drinking cup is 5.0 cm. The diameter of its mouth is 8.4 cm. The path of the cup curves when you roll it on top of the table. Which end, the base or the mouth rolls faster and how much faster?
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Answer #1

Given values are:

Diameter of base of cup(D1) = 5.0 cm

radius of base of cup(r1) = 5.0 /2 = 2.5 cm

Diameter of mouth of cup(D2) = 8.4 cm

radius of mouth of cup(r2) = 8.4 /2 = 4.2 cm

When cup rolls on top of the table angular speed of mouth(w1 )and base(w2) are equal

w1 = w2   

v1 / r1 = v2 / r2 (from the relation of linear velocity and angular velocity v = r w )

v2 / v1 =  r2 /r1

v2 = ( r2 /r1 ) * v1   eq(1)

here v1 and v2 are linear velocities of base of cup and mouth of cup

put the values of r1 and r2 in eq(1)

v2 = (4.2 / 2.5 ) * v1

v2 = 1.68 v1

Hence Mouth of Cup rolls 1.68 times faster than base of the cup

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