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A disk-shaped machine part has a diameter of 40.0 cm. Its angular position is given by
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Physics for Scientists and Engineers: Foundations and Connections
- Suppose when Earth was created, it was not rotating. However, after the application of a uniform torque after 6 days, it was rotating at 1 rev/day. (a) What was the angular acceleration during the 6 days? (b) What torque was applied to Earth during this period? (c) What force tangent to Earth at its equator would produce this torque?arrow_forwardA ball rolls to the left along a horizontal surface, up the slope, and then continues along a horizontal surface (Fig. P12.70). Sketch the angular speed and the magnitude of the angular acceleration of the ball as functions of time. FIGURE P12.70arrow_forwardA uniform cylinder of radius r = 10.0 cm and mass m = 2.00 kg is rolling without slipping on a horizontaltabletop. The cylinders center ofmass is observed to have a speed of 5.00 m/s at a given instant. a. What isthe translational kinetic energy of thecylinder at that instant? b. What is therotational kinetic energy of the cylinder around its center of mass at thatinstant? c. What is the total kineticenergy of the cylinder at that instant?arrow_forward
- During a very quick stop, a car decelerates at 7.00 m/s2. (a) What is the angular acceleration of its 0.280-m-radius tires, assuming they do not slip on the pavement? (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 95.0 rad/s? (c) How long does the car take to stop completely? (d) What distance does the car travel in this time? (e) What was the car's initial velocity? (f) Do the values obtained seem reasonable, considering that this stop happens very quickly?arrow_forwardIntegrated Concepts An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is its angular acceleration in rad/s2? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the radial acceleration in m/s2 and multiples of g of this point at full rpm?arrow_forwardA ball having mass m is fastened at the end of a flagpole that is connected to the side of a tall building at point P as shown in Figure P11.15. The length of the flagpole is , and it makes an angle with the x axis. The ball becomes loose and starts to fall with acceleration gj. (a) Determine the angular momentum of the ball about point P as a function of time. (b) For what physical reason does the angular momentum change? (c) What is the rate of change of the angular momentum of the ball about point P? Figure P11.15arrow_forward
- A pulsar is a rapidly rotating neutron star. The Crab nebula pulsar in the constellation Taurus has a period of 33.510-3s , radius 10.0 km, and mass 2.81030kg . The pulsar’s rotational period will increase over time due to the release of electromagnetic radiation, which doesn’t change its radius but reduces its rotational energy. (a) What is the angular momentum of the pulsar? (b) Suppose the angular velocity decreases at a rate of 1014rad/s2 . What is the torque on the pulsar?arrow_forwardLara is running just outside the circumference of a carousel, looking for her favorite horse to ride, with a constant angular speed of 1.00 rad/s. Just as she spots the horse, one-fourth of the circumference ahead of her, the carousel begins to move, accelerating from rest at 0.050 rad/s2. a. Taking the time when the carousel begins to move as t = 0, when will Lara catch up to the horse? b. Lara mistakenly passes the horse and keeps running at constant angular speed. If the carousel continues to accelerate at the same rate, when will the horse draw even with Lara again?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_forward
- A rotating objects angular position is given by (t) = (1.54t2 7.65t + 2.75) rad, where t is measured in seconds. Find a. the objects angular speed when t = 3.50 s and b. the magnitude of the angular acceleration when t = 3.50 s.arrow_forwardA system of point particles is shown in the following figure. Each particle has mass 0.3 kg and they all lie in the same place. (a) What is the moment of inertia of the system about the given axis? (b) If the system rotates at 5 rev/s, what is its rotational kinetic energy?arrow_forwardA vertical wheel with a diameter of 50 cm starts from rest and rotates with a constant angular acceleration of 5.0rad/s2 around a fixed axis through its center counterclockwise. (a) Where is the point that is initially at the bottom of the wheel at t=10s ? (b) What is the point’s linear acceleration at this instant?arrow_forward
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