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Angular Speed - Rotational Kinematics

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Learning Goal: To understand the meaning of the variables that appear in the equations for rotational kinematics with constant angular acceleration.

Rotational motion with a constant nonzero acceleration is not uncommon in the world around us. For instance, many machines have spinning parts. When the machine is turned on or off, the spinning parts tend to change the rate of their rotation with virtually constant angular acceleration. Many introductory problems in rotational kinematics involve motion of a particle with constant nonzero angular acceleration. The kinematic equations for such motion can be written as

teta(t) = teta_0 + omega_0*t + 1/2at^2 and .

Here, the meaning of the symbols is as follows:

teta is the angular position of the particle.
teta_0 is the initial angular position of the particle.
omega is the angular velocity of the particle.
omega_0 is the initial angular velocity of the particle.
a is the angular acceleration of the particle.

Consider two particles A and B. The angular position of particle A, with constant angular acceleration, depends on time according to

(when I write teta_0, I mean teta sub zero(initial..))

teta_A(t) = teta_0 + omega_0*t + 1/2at^2

At time t=t_1 , particle B, which also undergoes constant angular acceleration, has twice the angular acceleration, half the angular velocity, and the same angular position that particle A had at time t=0.

1) Give the equation that describes the angular position of particle B?

2 )How long after the time t_1 does the angular velocity of particle B equal that of particle A?

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