A 5 kg hoop (I=MR2) with a radius of 2 m is placed at the top of a hill that is 8 m high. There is just enough friction of the hoop to roll when it is released from rest. What is the hoop's translational (traveling) speed at the bottom of the hill? Please use 10 m/s2 for the magnitude of the acceleration due to gravity.

The crankshaft in a race car goes from rest to 3000 rpm in 2.0 seconds. How many revolutions does it make while reaching 3000 rpm?

Your roommate is working on his bicycle and has the bike upside down. He spins the 56.0 cmcm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What is the pebble's acceleration? Express your answer with the appropriate units.

There is a clever kitchen gadget for drying lettuce leaves after you wash them. It consists of a cylindrical container mounted so that it can be rotated about its axis by turning a hand crank. The outer wall of the cylinder is perforated with small holes. You put the wet leaves in the container and turn the crank to spin off the water. The radius of the container is 12.2 cm. When the cylinder is rotating at 2.45 revolutions per second, what is the magnitude of the centripetal acceleration at the outer wall? Number Units #

A light rod is 88 cm long. Its top end is pivoted on a low-friction horizontal axle. The rod hangs straight down at rest with a small massive ball attached to its bottom end. You strike the ball, suddenly giving it a horizontal velocity so that it swing around in full circle. What minimum speed (m/s) at the bottom is required to make the ball go over the top of the circle?   Round your answer to 2 decimal places.

A circular track has several concentric rings where people can run at their leisure. Phil runs on the outermost track with radius rP while Annie runs on an inner track with radius rA = 0.70 rP. The runners start side by side, along a radial line, and run at the same speed in a counterclockwise direction. How many revolutions has Annie made when Annie's and Phil's velocity vectors point in opposite directions for the first time?

A “blink of an eye” is a time interval of about 150 ms for an average adult. The “closure” portion of the blink takes only about 55 ms. Let us model the closure of the upper eyelid as uniform angular acceleration through an angular displacement of 15.4°. a. What is the value of the angular acceleration the eyelid undergoes while closing?  answer in rad/s^2 b. What is the tangential acceleration of the edge of the eyelid while closing if the radius of the eyeball is 1.25 cm? answerin m/s^2

A three-blade wind turbine, which spins perpendicularly to the ground, is set on a pole that is 38 m tall and completes 5 revolutions in one minute. The length of one blade is approximately 4 m long. One particular blade lies parallel to the ground before the turbine started to spin. a) What is the equation that models the height of tip of this blade as a function of time (in seconds)?

A 1.3 kg rock is swung in a circular path and in a vertical plane on a 1 m length string. At the top of the path, the angular velocity is 9 rad/s. What is the tension in the string at that point?

A disk spins at 4.0 revolutions/second. What is its period, in second? Your answer needs to have 2 significant figures, including the negative sign in your answer if needed. Do not include the positive sign if the answer is positive. No unit is needed in your answer, it is already given in the question statement.