1.

Two people start at the same place and walk around a circular lake in opposite directions. One has an angular speed of 1.14 x 10'3 rad/s, while the other has an angular speed of 8.44 x 10'3 rad/s. How long will it be before they meet? Number I Units v A dentist causes the bit of a high-speed drill to accelerate from an angular speed of 1.57 x 104 rad/s to an angular speed of 3.84 x 104 rad/s. In the process, the bit turns through 1.98 x 104 rad. Assuming a constant angular acceleration, how long would it take the bit to reach its maximum speed of 8.07 x 104 rad/s, starting from rest? Number n Units v An electricfan is running on HIGH. After the LOW button is pressed, the angular speed of the fan decreases to 89.2 rad/s in 2.72 s. The magnitude of the angular deceleration is 46.8 rad/52. Determine the initial angular speed of the fan. Number n Units V Suppose you are riding a stationary exercise bicycle, and the electronic meter indicates that the wheel is rotating at 11.6 rad/s. The wheel has a radius of 0.517 m. Ifyou ride the bike for 48.3 min, how far would you have gone if the bike could move? Number n Units V A man holds a 166-N ball in his hand, with the forearm horizontal (see the gure). He can support the ball in this position because of --) the exor muscle force M, which is applied perpendicular to the forearm. The forearm weighs 24.3 N and has a center of gravity as _) indicated. Find (a) the magnitude ofM and the (b) magnitude and (c) direction (as a positive angle counterclockwise from horizontal) of the force applied by the upper arm bone to the forearm at the elbowjoint. Upper arm bone 1 Flexor muscle I c Elbow 08 pint I I I 00510 mT'T' I0.0890 m l.00330 m1 I I I I I I (a) Number n Units v (b) Number n Units v (c) Number a Units v A clay vase on a potter's wheel experiences an angular acceleration of 6.92 rad/s due to the application of a 17.7-N m net torque. Find the total moment of inertia of the vase and potter's wheel. Number i UnitsA flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 365-mile trip in a typical midsize car produces about 1.90x 10' J of energy. How fast would a 38.5-kg flywheel with a radius of 0.427 m have to rotate to store this much energy? Give your answer in rev/min. Number i UnitsConceptual Example 14 provides useful background for this problem. A playground carousel is free to rotate about its center on frictionless bearings, and air resistance is negligible. The carousel itself (without riders) has a moment of inertia of 142 kg-mz. When one person is standing at a distance of 1.68 m from the center, the carousel has an angular velocity of 0.645 rad/s. However, as this person moves inward to a point located 0.763 m from the center, the angular velocity increases to 0.781 rad/s. What is the person's mass? Number n Units v