3. **Unicycle acceleration. Including terms that Taylor neglects, the equation of mo- tion in a noninertial...

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3. **Unicycle acceleration. Including terms that Taylor neglects, the equation of mo- tion in a noninertial frame is mr = F m(- dV dt + V) m r 2m 2m m ( r). (6) A unicycle travels with constant speed v around a track of radius p. The radius of the wheel is b. What is the acceleration of the highest point on the wheel? [Answer: (3v2/p)i (v/b)k.] Solve the problem two ways (as described below). (a) Use an inertial frame. Locate the horizontal center of the origin at the center of the track. Locate the vertical height of the origin at the height of the hub of the unicycle. Use (x, y) coordinates in the horizontal plane. The z direction is up. Write down the 7 coordinates in this frame, then find the acceleration. (b) Select the hub of the wheel as your noninertial frame. The x-axis points toward the center of the track and the z-axis points up. Use Eq. 6 to evaluate the acceleration in this frame. 3. **Unicycle acceleration. Including terms that Taylor neglects, the equation of mo- tion in a noninertial frame is mr = F m(- dV dt + V) m r 2m 2m m ( r). (6) A unicycle travels with constant speed v around a track of radius p. The radius of the wheel is b. What is the acceleration of the highest point on the wheel? [Answer: (3v2/p)i (v/b)k.] Solve the problem two ways (as described below). (a) Use an inertial frame. Locate the horizontal center of the origin at the center of the track. Locate the vertical height of the origin at the height of the hub of the unicycle. Use (x, y) coordinates in the horizontal plane. The z direction is up. Write down the 7 coordinates in this frame, then find the acceleration. (b) Select the hub of the wheel as your noninertial frame. The x-axis points toward the center of the track and the z-axis points up. Use Eq. 6 to evaluate the acceleration in this frame.