- #1

leafy

- 73

- 8

- Homework Statement
- Consider a wheel of large moment of inertia and radius. A mass is first allowed to descend with the wheel for a short distance as shown. It is then compared to the second case where it is free fall dropped for the same distance and make inelastic impact. The energy is the same for both cases.

Moment of inertia I = 10,000

Radius of the wheel r = 1000

Mass m = 2

Drop height h = 3

- Relevant Equations
- Mgh = .5mv^2

Mgh = .5(I)(w^2)

Ft = mv

Ftr = Iw

First case, descends with the wheel:

mgh = .5(I)(w^2) ———- GPE converted to wheel energy

w = .1095. ———- rotation result is .1095

Second case, allow to free fall and impulse:

mgh = .5(m)(v^2). ———- GPE converted to kinetic energy

v = 7.746 ———- result in speed of 7.746

Ft = mv ———— impulse when hit the wheel

Ftr = I(w) ———— impulse converted to angular momentum

w = 1.5491. ———— rotation result is 1.5491

is this correct?

mgh = .5(I)(w^2) ———- GPE converted to wheel energy

w = .1095. ———- rotation result is .1095

Second case, allow to free fall and impulse:

mgh = .5(m)(v^2). ———- GPE converted to kinetic energy

v = 7.746 ———- result in speed of 7.746

Ft = mv ———— impulse when hit the wheel

Ftr = I(w) ———— impulse converted to angular momentum

w = 1.5491. ———— rotation result is 1.5491

is this correct?