Chapter 8 Problems 23 or The quadratic formula yields t = 7.37 s and 42.6 s; therefore, the shortest time needed to catch the horse is . 34. REASONING The angular acceleration α gives rise to a tangential acceleration a T according to ( Equation 8.10). Moreover, it is given that a T = g , where g is the magnitude of the acceleration due to gravity. SOLUTION Let r be the radial distance of the point from the axis of rotation. Then, according to Equation 8.10, we have Thus, 35. REASONING AND SOLUTION
36.REASONINGThe tangential speed vTof a point on a rigid body rotating at an angular speed ϖis given by (Equation 8.9), where ris the radius of the circle described by the moving point. (In this equation ϖmust be expressed in rad/s.) Therefore, the angular speed of the bacterial motor sought in part ais . Since we are considering a point on the rim, rthe radius of the motor itself. In part b,we seek the elapsed timetfor an angular displacement of one revolution at the constant angular velocity ϖfound in part a. We will use (Equation 8.7) to calculate the elapsed time. is SOLUTION
Chapter 8 Problems 25 ϖ t .
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- Spring '10
- Angular velocity, Velocity, rad/s, angular displacement, θ moon