A ring is rolling on a horizontal surface without slipping. Find the ratio of translation kinetic energy to rotational kinetic energy of ring.

Solution

Let m be the mass and r be the radius of ring.
When the ring rolls without slipping, then v = rω,
where v is the velocity of centre of mass of ring, and
ω is its angular velocity.

Now the translational kinetic energy of the ring is,
$straight K subscript straight t space equals space 1 half mv squared space space space space space equals 1 half mr squared straight ϖ squared space$
Rotational kinetic energy of the ring is,
$straight K subscript straight r space equals 1 half Iϖ to the power of 2 space end exponent space space space space space equals space 1 half mr squared straight ϖ squared Therefore comma space the space ratio space o f space translational space to space rotational straight K. straight E space is space given space by comma space therefore space space straight K subscript t over straight K subscript r equals 1$

Some More Questions From Units and Measurement Chapter

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Units And Measurement

A ring is rolling on a horizontal surface without slipping. Find the ratio of translation kinetic energy to rotational kinetic energy of ring.

Some More Questions From Units and Measurement Chapter

Can we use different units to measure same physical quantity?

To measure a physical quantity X, the unit U is repeatedly used for n times. What is the magnitude of physical quantity?

Does the numerical factor in the quantitative measurement depend on the system of unit used?

Is one unit sufficient to measure a physical quantity?

Can a physical quantity have two or more units? Give example.

What are fundamental quantities?

How many fundamental quantities are there in mechanics?

How many fundamental quantities are there in Physics?

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