The unbalanced wheel has a mass of 15 kg and rolls without slipping on the flat horizontal surface. The wheel has a radius of gyration about its mass center G of 64 mm, and its mass center is 40 mm from the center of the wheel. When the mass center G passes the horizontal line through O, the angular velocity of the wheel is 4 rad/s. For this instant, compute:
a. The angular acceleration of the wheel.
b. The normal force N and the friction force F acting on the wheel at its point of contact with the horizontal surface.
c. The minimum coefficient of friction for which the wheel does not slip.

a)

b)

c)

Step-by-step explanation:

From the question we are told that

mass of unbalanced wheel

Radius of gyration

Mass center

Angular velocity

a)

Generally the equation for moment at point A is mathematically given as

Where

b)

Generally the equation for equilibrium of system on the horizontal axis is mathematically given as

c)

Generally the equation for equilibrium of system on the vertical axis is mathematically given as

Where

250

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.