Question

Two wheels initially at rest roll the same distance without slipping down identical planes. Wheel B has twice the radius, but the same mass as wheel A. All the mass is concentrated in their rims so that the rotational inertias are I = mR2. Which has more translational kinetic energy when it gets to the bottom?

Answer 1

Their translational kinetic energies are the same

Step-by-step explanation:

The translational kinetic energy of an object is given by the formula:

`KE = 0.5 mv^2`

Where m = the mass of the object and

v = the linear speed of the object

From the question, it is stated that wheel A has the same mass as wheel B, that is
`m_A = m_B`

Linear speed is also a function of the distance covered. Since both wheels cover the same distance within the same interval, we can conclude that
`v_A = v_B`

Both wheels A and B have equal speed and mass, this means that their translational kinetic energy is the same.

Note that translational kinetic energy is not a function of the radius