Exam 11: Motion in a Circle

The angular acceleration of a wheel is given in rad/s² by 45t³ - 11t⁴, where t is in seconds.If the wheel starts from rest at t = 0.00 s,when is the next time the wheel is at rest?

For an object in uniform circular motion,its velocity and acceleration vectors are always perpendicular to each other at every point in the path.

An aircraft performs a maneuver called an "aileron roll." During this maneuver,the plane turns like a screw as it maintains a straight flight path,which sets the wings in circular motion.If it takes it 35 s to complete the circle and the wingspan of the plane is 11 m,what is the acceleration of the wing tip?

The angular velocity of a 755-g wheel 15.0 cm in diameter is given by the equation ω(t)= (2.00 rad/s²)t + (1.00 rad/s⁴)t³. (a)Through how many radians does the wheel turn during the first 2.00 s of its motion? (b)What is the angular acceleration (in rad/s²)of the wheel at the end of the first 2.00 s of its motion?

Future space stations will create an artificial gravity by rotating.Consider a cylindrical space station 390 m diameter rotating about its central axis.Astronauts walk on the inside surface of the space station.What rotation period will provide "normal" gravity?

An object moves in a circle of radius R at constant speed with a period T.If you want to change only the period in order to cut the object's acceleration in half,the new period should be

A car travels at a steady 40.0 m/s around a horizontal curve of radius 200 m. What is the minimum coefficient of static friction between the road and the car's tires that will allow the car to travel at this speed without sliding?

A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down.If the radius of the loop is 13.2 m,with what minimum speed must the car traverse the loop so that the rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.

Two particles,A and B,are in uniform circular motion about a common center.The acceleration of particle A is 8.5 times that of particle B.The period of particle B is 2.0 times the period of particle A.The ratio of the radius of the motion of particle A to that of particle B is closest to

A car enters a 300-m radius horizontal curve on a rainy day when the coefficient of static friction between its tires and the road is 0.600. What is the maximum speed at which the car can travel around this curve without sliding?

When a rigid body rotates about a fixed axis,all the points in the body have the same

A 3.45-kg centrifuge takes 100 s to spin up from rest to its final angular speed with constant angular acceleration. A point located 8.00 cm from the axis of rotation of the centrifuge moves with a speed of 150 m/s when the centrifuge is at full speed. (a)What is the angular acceleration (in rad/s²)of the centrifuge as it spins up? (b)How many revolutions does the centrifuge make as it goes from rest to its final angular speed?

A turntable has a radius of 0.80 m and a moment of inertia of 2.0 kg • m².The turntable is rotating with an angular velocity of 1.5 rad/s about a vertical axis though its center on frictionless bearings.A very small 0.40-kg ball is projected horizontally toward the turntable axis with a velocity of 3.0 m/s.The ball is caught by a very small and very light cup-shaped mechanism on the rim of the turntable (see figure).What is the angular velocity of the turntable just after the ball is caught?

In the figure,point P is at rest when it is on the x-axis.The linear speed of point P when it reaches the y-axis is closest to