A car is accelerating from rest.  There is a 1.6 g pebble stuck in the tread of one of the tires 0.38 m from the center of rotation. The pebble is held in place with static friction which has a maximum value of 3.6 N. What speed does the car reach when the pebble pulls out of the tread?  Use Newton's 2nd Law and centripetal acceleration to solve this.  Think about the relationship between the translational speed of the car and the tangent speed of the pebble.

A 50.0 kg child stands at the rim of a merry-go-round of radius 1.70 m, rotating with an angular speed of 2.95 rad/s. (a) What is the child's centripetal acceleration? m/s2(b) What is the minimum force between her feet and the floor of the carousel that is required to keep her in the circular path? N(c) What minimum coefficient of static friction is required?Is the answer you found reasonable? In other words, is she likely to stay on the merry-go-round?

A rock tied to the end of string swings at a constant angular rate. If you are told that the string can support a total of 85 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.16 kg, and the length of the string is 0.5 m? Give your answer in units of radian per second

It has been suggested that rotating cylinders about 20.0 mi long and 5.49 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?                                                                                             rad/s

A van with mass m = 1000 kg is driving around a circular curve of radius r = 950 m when it begins to rain. The coefficients of static friction between the track and tires is μd = 0.59 when dry and μw = 0.17 when wet. Write an expression for the maximum magnitude of the force of static friction Ff acting on the van if μs is the coefficient of friction. What is the maximum tangential speed that the van can take the corner at without slipping when dry in m/s? What is the maximum tangential speed when wet in m/s?

Imagine If A skateboarder is attempting to make a circular arc of radius r = 19 m in a parking lot. We know the total mass of the skateboard and skateboarder is m = 95 kg. If the coefficient of static friction between the surface of the parking lot and the wheels of the skateboard is μs = 0.66 . A) Now what is the maximum speed, in meters per second, he can travel through the arc without slipping?

A car is undergoing an emissions test. The car is stationary on rollers while the gas pedal is depressed until the speedometer reads 60 km/h. The wheels are 54 cm in diameter. Find their angular speed.

A student is whirling a ball on a string in a circle with an angular speed of 20 rad/s.  Air drag decelerates the ball at a rate of -3 rad/s2.  What is the angular speed of the ball after it has spun through an angle of 30 radians? Remember to include units with your answer.   A disk is initially at rest.  If the disk speeds up uniformly to a speed of 45 rad/s in a time of 15 seconds, what angle does it turn through? Remember to include units with your answer.

A 2 m rope attaches a tire to an overhanging tree limb. A boy swinging on the tire has a tangential speed of 2.2 m/s. If the magnitude of the centripetal force is 90 N; what is the boy mass?

You are swinging a 0.45 kg water balloon vertically. The distance from your shoulder (acting as the center of rotation) and the water balloon is about 0.70 m. You estimate the water balloon is traveling at 6.0 m/s. At the very bottom of the circular path, how much force is your hand holding the water balloon?