A parent exerts a torque on a merry-go-round at a park. The torque has a magnitude given by
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Physics for Scientists and Engineers: Foundations and Connections
- A cam of mass M is in the shape of a circular disk of diameter 2R with an off-center circular hole of diameter R is mounted on a uniform cylindrical shaft whose diameter matches that of the hole (Fig. P1 3.78). a. What is the rotational inertia of the cam and shaft around the axis of the shaft? b. What is the rotational kinetic energy of the cam and shaft if the system rotates with angular speed around this axis?arrow_forwardTo develop muscle tone, a woman lifts a 2.00-kg weight held in her hand. She uses her biceps muscle to flex the lower arm through an angle of 60.0°. (a) What is the angular acceleration if the weight is 24.0 cm from the elbow joint, her forearm has a moment of inertia of 0.250kg-m2 and the net force she exerts is 750 N at an effective perpendicular lever arm of 2.00 cm? (b) How much work does she do?arrow_forwardThe mass of a hoop of radius 1.0 m is 6.0 kg. It rolls across a horizontal surface with a speed of 10.0 m/s. (a) How much work is required to stop the hoop? (b) If the hoop starts up a surface at 30 to the horizontal with a speed of 10.0 m/s, how far along the incline will it travel before stopping and rolling back down?arrow_forward
- Consider again the two wind turbines in Problem 32. a. At what point along the 40-m blade would the angular distance traveled by the point be the same as the angular distance traveled by the point at the end of the 20-m blade? b. At what point along the 40-m blade would the translational distance traveled by the point be the same as the translational distance traveled by the point at the end of the 20-m blade?arrow_forwardThe axis of Earth makes a 23.5 angle with a direction perpendicular to the plane of Earth’s orbit. As shown below, this axis precesses, making one complete rotation in 25,780 y. (a) Calculate the change in angular momentum in half this time. (b) What is the average torque producing this change in angular momentum? (c) If this torque were created by a pair of forces acting at the most effective point on the equator, what would the magnitude of each force be?arrow_forwardA bug of mass 0.020 kg is at rest on the edge of a solid cylindrical disk (M=0.10kg,R=0.10m) rotating in a horizontal plane around the vertical axis through its center. The disk is rotating at 10.0 rad/s. The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of the disk, what is the angular velocity of the disk then? (d) What is the new kinetic energy of the system? (e) What is the cause of the increase and decrease of kinetic energy?arrow_forward
- The rigid body shown in the figure consists of three particles connected by massless rods. It is to be rotated about an axis perpendicular to its plane through point P. If M = 0.41 kg, a = 35 cm, and b = 53 cm, how much work is required to take the body from rest to an angular speed of 5.8 rad/s? M 2M Number Units Jarrow_forwardThe following figure shows the cross section of a cylinder of radius 8.8 m rotating about its axis at 4.0 rad/s. The :speed of the point P is rad/s 110.58 .a O m/s 110.58 .b O rad/s 35.20 .c O Can not be determined .d O m/s 35.20 .e Oarrow_forwardA horizontal 800-N merry-go-round is a solid disk of radius 1.50 m and is started from rest by a constant horizontal force of 50.0 N applied tangentially to the edge of the disk. Find the kinetic energy of the disk after 3.00 s? A. 200 J В. 320 J С. 276 J D. 210 J E. 400 Jarrow_forward
- A particle of mass m is attached to the end of a string and moves in a circle of radius r on a frictionless horizontal table. The string passes through a frictionless hole in the table and, initially, the other end is fixed. a. If the string is pulled so that the radius of the circular orbit decreases, how does the angular velocity change if it is wo when r = ro? 6. b. What work is done when the particle is pulled slowly in from a radius ro to a radius ro/2?arrow_forwardPeter propels a penguin with mass 10.0kg from 2.50m above the ground at an angle 30.0o from the horizontal axis (ground), with an initial speed of 15.0 m/s. Assuming the penguin remains rigid (scared, so assume the particle model!) and ignoring any rotational effects, Using the isolated system model, what is the maximum potential energy of the penguin? a. 1370 Joules b. 1125 Joules c. 245 Joules d. 2250 Joulesarrow_forwardOne way to store energy is in the rotational motion of a flywheel, and some have proposed using such technology to power automobiles. One unit is based on a 7.0-kg flywheel in the shape of a hoop of radius 0.12 m that spins as fast as 50000 rpm A. How much kinetic energy is stored by the flywheel when it is rotating at its maximum rate? Express your answer to two significant figures and include appropriate units. B. If the vehicle requires an average power of 13 kW under normal driving conditions, for how much time can it operate with the energy stored in the flywheel? Express your answer to two significant figures and include appropriate units.arrow_forward
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