(b) Given that Icm = ½MR2 for a uniform solid wheel,

Question

(i) show that the rotational kinetic energy is half the translational kinetic energy for such a wheel.
(ii) For the wheel of diameter 10 cm, find its final speed after traversing a distance of 10 m down an incline of 25º. Assume it starts from rest.
(iii) How long does it take to do this?
(iv) Which will travel faster down the slope: A uniform solid wheel or a hoop?
(v) Evaluate the time for the solid hoop to roll down the 10 m.

Answer 1

You need to show some effort of your own here. here is the way to proceed.

i) Use the facts that V = R w
and I = (1/2) M R^2
Compare (1/2) R V^2 with (1/2) I w^2, after substituting for I and w.

ii) Apply conservation of energy, making sure you count both translational and rotational KE

iii) Compute final speed at the bottom using the final kinetic energy. The average speed is half that. T = distance travelled/(average speed)

iv) Use same approach, but the appropriate moment of inertia formula

v) Same apprach as iii)

Answer 2

ii) Apply conservation of energy, making sure you count both translational and rotational KE

now with this part Im not sure what you mean?
i understand the conservation of energy but that wont give me the speed of the wheel