1. A grindstone of radius 4.0 m is initially spinning with anangular speed of 8.

Question

1. A grindstone of radius 4.0 m is initially spinning with anangular speed of 8.0 rad/s. The angular speed is then increased to12 rad/s over the next 4.0 seconds. Assume that the angularacceleration is constant. Through how many revolutions doesthe grindstone turn during the 4.0-second interval?
2.A wheel of radius 0.5 mrotates with a constant angular speed about an axis perpendicularto its center. A point on the wheel that is 0.2 m from the centerhas a tangential speed of 2 m/s. Determine the tangentialspeed of a point 0.3 m from the center of the wheel.
3. On an amusement parkride, passengers are seated in a horizontal circle of radius 7.5 m.The seats begin from rest and are uniformly accelerated for 21seconds to a maximum rotational speed of 1.4 rad/s.What is thetangential acceleration of the passengers during the first 21 s ofthe ride?
2.A wheel of radius 0.5 mrotates with a constant angular speed about an axis perpendicularto its center. A point on the wheel that is 0.2 m from the centerhas a tangential speed of 2 m/s. Determine the tangentialspeed of a point 0.3 m from the center of the wheel.
3. On an amusement parkride, passengers are seated in a horizontal circle of radius 7.5 m.The seats begin from rest and are uniformly accelerated for 21seconds to a maximum rotational speed of 1.4 rad/s.What is thetangential acceleration of the passengers during the first 21 s ofthe ride?

Explanation / Answer

Rdius R = 4. m
Initial angular speed w = 8 rad / s final angular speed w ' = 12 rad / s time t= 4 s Angular accleration = ( w' - w ) / t = 1 rad / s^ 2 angular displacment in tht time = [ w ' ^ 2- w ^2] / 2                                                  = 40 rad (2). Radius r = 0.5 m distance r ' = 0.2 m Tangential speed v = 2 m / s Angular speed   w = v / r ' = 10 rad / s Tangential speed at r " = 0.3 m is   v ' = r "* w = 3 m / s

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