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## Homework Statement

The rotating subunits forms an approximately cylindrical axel with a diameter of 4 nm and total mass of 80,000 Daltons. The motor takes three steps per revolution with each step taking 0.067 s. We can model the rotating subunits as a rotating cylinder and use the properties described above to calculate:

A. The angular acceleration of the motor during each step (Assume the motor pauses very briefly between steps and therefore starts each step from rest)

B. The torque needed to generate the acceleration calculated in (a). Hint: you will need to determine the moment of inertia first.

## Homework Equations

A. Angular acceleration = change in angular velocity/ time interval

Angular velocity = 2 X pi radians X F

F=1/period

B. Torque = rF

Using the answer we found in part A the equation would be: angular acceleration = Torque/mr^2

## The Attempt at a Solution

A. Period = 0.067 s X 3 steps = .201 s

Frequency= 1/period = 1/.201s = 4.97512 s^-1

angular velocity = 2 X pi X 4.97512 s-1 = 31.2592 rad s-1

so angular acceleration = 31.2592 rad s-1 / 0.067 s - 0 s = 466.561 rads-2

B. 4nm=.000000004 m = diameter

.000000002 m = radius

80000 Daltons = 1.328 X 10 ^-22 kg

466.561 rad s^-2 = Torque/ (1.328 x 10^-22 kg) (.000000002 m)^2

= 2.47837 x 10^-37 Nxm