A uniform sphere of radius 4.25 cm and a uniform spherical shell of radius 7.00 cm are rolling without slipping along the same floor. The two objects have the same mass. If they have the same total kinetic energy, determine the ratio of the sphere's angular speed ωsph to the spherical shell's angular speed ωshl . ωsph ωshl =
A car is traveling along a road, and its engine is turning over with an angular velocity of +200 rad/s. The driver steps on the accelerator, and in a time of 8.0 s the angular velocity increases to +290 rad/s. (a) What would have been the angular displacement of the engine if its angular velocity had remained constant at the initial value of +200 rad/s during the entire 8.0 - s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +290 rad/s during the entire 8.0−s interval? (c) Determine the actual value of the angular displacement during the 8.0-5 interval. (a) θ = (b) θ = (c) θ =