A race car starts from rest on a circular track. The car increases its speed at a constant rate at as it goes once around the track. Find the angle that the total accelera- tion of the car makes—with the radius connecting the center of the track and the car—at the moment the car completes the circle.

The “mean” orbital radius listed for astronomical objects orbiting the Sun is typically not an integrated average but is calculated such that it gives the correct period when applied to the equation for circular orbits. Given that, what is the mean orbital radius in terms of aphelion and perihelion?

As their booster rockets separate, Space Shuttle astronauts typically feel accelerations up to 3g, where g = 9.80 m/s2. In their training, astronauts ride in a device where they experience such an acceleration as a centripetal acceleration. Specifically, the astronaut is fastened securely at the end of a mechanical arm, which then turns at constant speed in a horizontal circle. Determine the rotation rate, in revolutions per second, required to give an astronaut a centripetal acceleration of 3.00g while in circular motion with radius 9.45 m.

Can tangential acceleration change the speed of a particle undergoing circular motion?

Check Your Understanding A flywheel has a radius of 20.0 cm What is the speed of a point on the edge of the flywheel if it experiences a centripetal acceleration of 900.0cm/s2 ?

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as shown in Figure P7.15. The length of the arc ABC is 235 m, and the car completes the turn in 36.0 s. (a) Determine the cars speed. (b) What is the magnitude and direction of the acceleration when the car is at point B? Figure P7.15

In Example 2.6, we considered a simple model for a rocket launched from the surface of the Earth. A better expression for the rockets position measured from the center of the Earth is given by y(t)=(R3/2+3g2Rt)2/3j where R is the radius of the Earth (6.38 106 m) and g is the constant acceleration of an object in free fall near the Earths surface (9.81 m/s2). a. Derive expressions for vy(t) and ay(t). b. Plot y(t), vy(t), and ay(t). (A spreadsheet program would be helpful.) c. When will the rocket be at y=4R? d. What are vy and ay when y=4R?

A propeller blade at rest starts to rotate from t=0 to t=5.0s with a tangential acceleration of the tip of the blade at 3.00m/s2 . The tip of the blade is 1.5 m from the axis of rotation. At t=5.0s , what is the total acceleration of the tip of the blade?

An experimental jet rocket travels around Earth along its equator just above its surface. At what speed must the jet travel if the magnitude of its acceleration is g ?

The CERN particle accelerator is circular with a circumference of 7.0 km. (a) What is the acceleration of the protons (m=1.671027kg)that move around the accelerator at 5of the speed of light? (The speed of light is v=3.00108m/s .) (b) What is the force on the protons?