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Consider an amusement park ride in which participants are rotated about a vertical axis in a cylinder with vertical walls. Once the
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- While punting a football, a kicker rotates his leg about the hip joint. The moment of inertia of the leg is 3.75kgm2 and its rotational kinetic energy is 175 J. (a) What is the angular velocity of the leg? (b) What is the velocity of tip of the punter’s shoe if it is 1.05 m from the hip joint?arrow_forwardAn air puck of mass m1 = 0.25 kg is tied to a siring and allowed to revolve in a circle of radius R = 1.0 m on a frictionless horizontal table. The other end of the string passes through a hole in the center of the table, and a mass of m2 = 1.0 kg is tied to it (Fig. P7.27). The suspended mass remains in equilibrium while the puck on the tabletop revolves, (a) What is the tension in the string? (b) What is the horizontal force acting on the puck? (c) What is the speed of the puck? Figure P7.27arrow_forwardKeratinocytes are the most common cells in the skins outer layer. As these approximately circular cells migrate across a wound during the healing process, they roll in a way that reduces the frictional forces impeding their motion. (a) Given a cell body diameter of 1.00 105 m (10 m), what minimum angular speed would be required to produce the observed linear speed of 1.67 107 m/s (10 m/min)? (b) How many complete revolutions would be required for the cell to roll a distance of 5.00 103 m? (Because of slipping as the cells roll, averages of observed angular speeds and the number of complete revolutions are about three times these minimum values.)arrow_forward
- In 2015, in Warsaw, Poland, Olivia Oliver of Nova Scotia broke the world record for being the fastest spinner on ice skates. She achieved a record 342 rev/min, beating the existing Guinness World Record by 34 rotations. If an ice skater extends her aims at that rotation rate, what would be her new rotation rate? Assume she can be approximated by a 45-kg rod that is 1.7 m tall with a radius of 15 cm in the record spin. With her aims stretched take the approximation of a rod of length 130 cm with 10 of her body mass aligned perpendicular to the spin axis. Neglect frictional forces.arrow_forwardThe angular position of a rod varies as 20.0t2radians from time t=0 . The rod has two beads on it as shown in the following figure, one at 10 cm from the ratation axis and the other at 20 cm from the rotation axis. (a) What is the instantaneous angular velocity of the rod at t=5s ? (b) What is the angular acceleration of the rod? (c) What are the tangential speeds of the beads at t=5s ? (d) What are the tangential acceleration of the beads at t=5s ? (e) What are the centripetal accelerations of the beads at t=5s ?arrow_forwardConsider an object on a rotating disk a distance r from its center, held in place on the disk by static friction. Which of the following statements is not true concerning this object? (a) If the angular speed is constant, the object must have constant tangential speed. (b) If the angular speed is constant, the object is not accelerated. (c) The object has a tangential acceleration only if the disk has an angular acceleration. (d) If the disk has an angular acceleration, the object has both a centripetal acceleration and a tangential acceleration. (e) The object always has a centripetal acceleration except when the angular speed is zero.arrow_forward
- A 4.0-kg particle moves in a circle of radius 2.0 m. The angular momentum of the particle varies in time according to l=5.0t2 , (a) What is the torque on the particle about the center of the circle at t=3.4s ? (b) What is the angular velocity of the particle at t=3.4s ?arrow_forwardA proton is accelerated in a cyclotron to 5.0106m/s in 0.01 s. The proton follows a circular path. If the radius of the cyclotron is 0.5 km, (a) What is the angular momentum of the proton about the center at its maximum speed? (b) What is the torque on the proton about the center as it accelerates to maximum speed?arrow_forwardOn takeoff, the propellers on a UAV (unmanned aerial vehicle) increase their angular velocity form rest at a rate of =(25.0t)rad/s for 3.0 s. (a) What is the instantaneous angular velocity of the propellers at t=2.0s ? (b) What is the angular acceleration?arrow_forward
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