heoretical value % Difference QUESTIONS 1. If two objects have the same mass and

Question

heoretical value % Difference QUESTIONS 1. If two objects have the same mass and angular velocity but one has twice the radius of rotation of the other, by what factor do their kinetics differ? (HINT: See Eq. 3) If the ring and the disk had the same outer radius and mass which would roll down an inclined plane faster? Why? 2. If a wheel slides without rolling down a frictionless inclined plane how would the time to reach the bottom compare to the identical wheel rolling down the identical plane but with friction present? Why? 3.

Explanation / Answer

1) one has 4 times the kinetic energy of the other.

As v = r*w =====> v1/v2 = 2 [Because w1 = w2, r1 = 2r2]

So, K1/K2 = m1v1^2/m2v2^2 = (v1/v2)^2 [Because m1 = m2]

K1/K2 = 4

2) The disk, because it will accelerate faster than the ring. The ring has the mass concentrated at the rim, far from the center; the further from the center the mass is, the harder it is to overcome rotational inertia. Bike wheels with heavy rims and mud tires are harder to spin up than light rims and racing tires.

So the solid disk has lower rotational inertia and accelerates faster, even with same mass, contact patch, and rolling friction.

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