A wheel of radius 0.5 m rotates with a constant angular speed about axis perpend

Question

A wheel of radius 0.5 m rotates with a constant angular speed about axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. (a) Determine the angular speed of the wheel. (b) Determine the tangential speed of a point 0.3 m from the center of the wheel. (c) Determine the tangential acceleration of the point that is 0.2 m from the center. The angular speed of the rotor in a centrifuge increases from 630 to 1420 rad/s in a 5.00 s. (a) Obtain the angle through which the rotor turns. (b) What is the magnitude of the angular acceleration?

Explanation / Answer

here,

9)

radius , r = 0.5 m

vt = 2 m/s

x= 0.2 m

a)

the angular speed of the wheel , w = vt /x = 2/0.2 rad/s = 10 rad/s

b)

the tangential speed at a = 0.3 m , vt = a * w = 0.3 * 10 rad/s = 3 m/s

c)

the tangential accelration at x = 0.2 m , ac = vt^2 /x

ac = 2^2 /0.2 = 20 rad/s^2

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