A car with a total mass of 1000 kg has four wheels, each of 10 kg. When the car is moving (rolling without slipping), what fraction of its total kinetic energy is due to the rotation of the wheels around their axis? a) Give a final formula for Erot / Exin total . b) Plug in numbers and give the ratio. Hints: What mass(es) do you have to use for kinetic energy and rotational energy? Assume that the wheels can be described as full solid cylinders and look up the moment of inertia of those cylinders.

A car with a total mass of 1000 kg has four wheels, each of 10 kg. When the car is moving (rolling without slipping), what fraction of its total kinetic energy is due to the rotation of the wheels around their axis? a) Give a final formula for Erot / Exin total . b) Plug in numbers and give the ratio. Hints: What mass(es) do you have to use for kinetic energy and rotational energy? Assume that the wheels can be described as full solid cylinders and look up the moment of inertia of those cylinders.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter8: Rotational Equilibrium And Dynamics

Section8.5: Rotational Kinetic Energy

Problem 8.4QQ: Two spheres, one hollow and one solid, are rotating with the same angular speed around an axis...

See similar textbooks

Similar questions

Consider two objects with m1 m2 connected by a light string that passes over a pulley having a moment of inertia of I about its axis of rotation as shown in Figure P10.44. The string does not slip on the pulley or stretch. The pulley turns without friction. The two objects are released from rest separated by a vertical distance 2h. (a) Use the principle of conservation of energy to find the translational speeds of the objects as they pass each other. (b) Find the angular speed of the pulley at this time.
The blades of a wind turbine are 30 m in length and rotate at a maximum rotation rate of 20 rev/min. (a) If the blades are 6000 kg each and the rotor assembly has three blades, calculate the angular momentum of the turbine at this rotation rate. (b) What Is the torque require to rotate the blades up to the maximum rotation rate in 5 minutes?
A 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?
An athlete in a gym applies a constant force of 50 N to the pedals of a bicycle to keep the rotation rate of the wheel at 10 rev/s. The length of the pedal arms is 30 cm. What is the power delivered to the bicycle by the athlete?
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?
While exercising in a fitness center, a man lies face down on a bench and lifts a weight with one lower leg by contacting the muscles in the back of the upper leg. (a) Find the angular acceleration produced given the mass lifted is 10.0 kg at a distance of 28.0 cm from the knee joint, the moment of inertia of the lower leg is 0.900kg-m2 the muscle force is 1500 N, and its effective perpendicular lever arm is 3.00 cm. (b) How much work is done if the leg rotates through an angle of 20.0° with a constant force exerted by the muscle?
A wheel is rotating about a fixed axis with constant angular acceleration 3 rad/s2. At different moments, its angular speed is 2 rad/s, 0. and +2 rad/s. For a point on the rim of the wheel, consider at these moments the magnitude of the tangential component of acceleration and the magnitude of the radial component of acceleration. Rank the following five items from largest to smallest: (a) |at| when = 2 rad/s, (b)|ar| when = 2 rad/s, (c)|ar| when = 0, (d) |at| when = 2 rad/s, and (e) |ar| when = 2 rad/s. If two items are equal, show them as equal in your ranking. If a quantity is equal to zero, show that fact in your ranking.
A 40.0-kg solid cylinder is rolling across a horizontal surface at a speed of 6.0 m/s. How much work is required to stop it?
A diver goes into a somersault during a dive by tucking her limbs. If her rotational kindetic energy is 100 J and her moment of inertia in the tuck is 9.0kgm2 , what is her rotational rate during the somersault?
Two spheres, one hollow and one solid, are rotating with the same angular speed around an axis through their centers. Both spheres have the same mass and radius. Which sphere, if either, has the higher rotational kinetic energy? (a) The hollow I sphere, (b) The solid sphere, (c) They have the same kinetic energy.
A uniform cylindrical grindstion has a mass of 10 kg and a radius of 12 cm. (a) What is the rotational kinetic energy of the grindstone when it is rotating at 1.5103rev/min ? (b) After the grindstone’s motor is turned off, a knife blade is pressed against the outer edge coefficient of kinetic friction between the grindstone and the blade is 0.80. Use the work energy theorem to determine how many turns the grindstone makes before it stops.
A tennis ball is a hollow sphere with a thin wall. It is set rolling without slipping at 4.03 m/s on a horizontal section of a track as shown in Figure P10.62. It rolls around the inside of a vertical circular loop of radius r = 45.0 cm. As the ball nears the bottom of the loop, the shape of the track deviates from a perfect circle so that the ball leaves the track at a point h = 20.0 cm below the horizontal section. (a) Find the balls speed at the top of the loop. (b) Demonstrate that the ball will not fall from the track at the top of the loop. (c) Find the balls speed as it leaves the track at the bottom. What If? (d) Suppose that static friction between ball and track were negligible so that the ball slid instead of rolling. Would its speed then be higher, lower, or the same at the top of the loop? (e) Explain your answer to part (d). Figure P10.62