Wheels A and B have weights of 150 lb and 100 lb , respectively. Initially, wheel A rotates clockwise with a constant angular velocity of 100 / A   rad s and wheel B is at rest. If A is brought into contact with B, determine the time required for both wheels to attain the same angular velocity. The coefficient of kinetic friction between the two wheels is 0.3 k  and the radii of gyration of A and B about their respective centers of mass are 1 A k ft  and 0.75 B k ft . Neglect the weight of link AC.

The image attached that is supposed to be attached to the question is shown in the first file below.

t = 2.19 seconds

Explanation:

The free body diagram showing the center of mass A and B is attached in the second diagram below.

NOTE : that from the second diagram; Mass A and B do not have any acceleration

Taking the moment about wheel A:

The equilibrium forces in the y-direction is 0

i.e

So;

The equilibrium forces in the x-direction is as follows:

The kinetic friction f can be expressed as :

From above equation (2) and equation (3);

N = 181.423 lb

Similarly; from equation(1)

However; from the kinematics ; as moments are constant ; so is the angular acceleration is constant )

Thus;

Let's take a look at wheel B now;

Taking the moment about wheel B from the equation of motion:

Again; from the kinematics; as the moments are constant which lead to the angular accleration;

From equation 4 and 5 which attain the same angular velocity; we have;

100 - 14.6045 t = 31.1563 t

100 = 31.1563 t + 14.6045 t

100 = 45.761 t

t = 100/45.761

t = 2.19 seconds

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explanation:

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explanation:

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