You are sitting on the edge of a horizontal disk (for example, a playground merry-go-round) that has radius 3.00 m and is rotating at a constant rate about a vertical axis. (a) If the coefficient of static friction between you and the surface of the disk is 0.400, what is the minimum time for one revolution of the disk if you are not to slide off? (b) Your friend’s weight is half yours. If the coefficient of static friction for him is the same as for you, what is the minimum time for one revolution if he is not to slide off?

In the figure, block 1 has mass m₁ - 470 g, block 2 has mass m₂ - 501 g, and the pulley is on a frictionless horizontal axle and has radius R-5.00 cm. When released from rest, block 2 falls 72.0 cm in 3.30 s without the cord slipping on the pulley. (a) What is the magnitude of the acceleration of the blocks? What are (b) tension T₂ (the tension force on the block 2) and (c) tension T₁ (the tension force on the block 1)? (d) What is the magnitude of the pulley's angular acceleration? (e) What is its rotational inertia? Caution: Try to avoid rounding off answers along the way to the solution. Use g -9.81 m/s². (a) Number (b) Number i (c) Number (d) Number i (e) Number i Units Units Units Units Units my 1112 <

A vehicle weighing 500 kilograms travels on a round banked highway that is inclined at angle of theta=20 and has a radius of 100 m at one speed. This is the quickest the vehicle can go without sliding up or down the hill. If the static friction force is high enough to allow the vehicle to handle the curve, what is the one speed at which the car can go without sliding down?