Question

# A disk-shaped machine part has a diameter of 39.0 cm. Its angular position is given by...

A disk-shaped machine part has a diameter of 39.0 cm. Its angular position is given by

θ = −1.22t3 + 1.60t2,

where t is in seconds and θ is in radians.

(a) What is the maximum angular speed of the part during this time interval? (Assume the time interval is from t = 0 to when the part reverses its direction.)

(b) What is the maximum tangential speed of a point halfway to the rim of the part during this time interval?
m/s

(c) What is the time t for which the part reverses its direction of motion after

t = 0?

s

(d) Through how many revolutions has the part turned when it reaches the time found in part (c)?
revolutions

a) given

then angular speed is

and angular acceleration is

a) Angular speed is maximum when a = 0

Therefore

or

b) diameter is d = 0.39 m

the maximum tangential speed of a point d/4 at t = 0.437 s is

c) the time for which the part reverses its direction of motion is when theta = 0

or

d) The total angular displacement during this time is

The number of revolutions is

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