Exam 5: Circular Motion

A 5,000 kg satellite is orbiting the Earth in a geostationary orbit. The height of the satellite above the surface of the Earth is (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 2.0 seconds from the start?

An object is moving in a circular path of radius 4.00 m. If the object moves through an angle of 1.2 radians, then the tangential distance traveled by the object is

A CD has a diameter of 12.0 cm and is rotating at an angular velocity of 10.0 rad/sec. If the CD has a constant angular acceleration of −0.5 rad/sec², then the angular velocity of the CD after 3.0 sec is

A conical pendulum is constructed by attaching a mass to a string 2.00 m in length. The mass is set in motion in a horizontal circular path about the vertical axis. If the angle the string makes with the vertical axis is 45.0 degrees, then the angular speed of the conical pendulum is

An object is moving in a circular path of radius R. If the object moves through an angle of 30 degrees, then the angle in radians is

A 4,000 kg satellite is traveling in a circular orbit 200 km above the surface of the Earth. A 30.0 gram marble is dropped inside the satellite. What is the magnitude of the acceleration of the marble as viewed by the observers inside the satellite? (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 3.18 Hz, then the period of the rotational motion is

A CD with a diameter of 12.0 cm starts from rest and with a constant angular acceleration of 1.0 rad/sec² acquires an angular velocity of 5.0 rad/sec. The CD continues rotating at 5.0 rad/sec for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the radial acceleration of a point 4.0 cm from the center at the time 10.0 seconds from the start?

A CD has a diameter of 12.0 cm. If the CD is rotating with a constant period of 0.314 seconds, then the frequency of the rotational motion is

An object is moving in a circular path with a radius of 5.00 m. If the object moves through an angle of 270 degrees, then the tangential distance traveled by the object is

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 20.0 radians per second, then the frequency of the rotational motion is

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant angular speed of 20 radians per second, then the linear speed of a point on the circumference is

A 4,000 kg satellite is traveling in a circular orbit 200 km above the surface of the Earth. A 30.0 gram marble is dropped inside the satellite. What is the magnitude of the acceleration of the marble as viewed by the observers on the Earth? (M_E = 5.98 × 10²⁴ kg, R_E = 6.37 × 10⁶ m, G = 6.67 × 10⁻¹¹ N·m²/kg²)

A roller coaster has a vertical loop with radius 29.5 m. What is the minimum speed of the roller coaster car at the top of the loop if the passengers do not lose contact with the seats?

When a girl swings in a tire swing, the tangential acceleration in the rope

A car travels on a road that, if viewed from the side, has a semicircular bump. When at the top of the bump, the occupants of the car feel as though they weigh half their normal weight. What is the speed of the car if the radius of the semicircle is 120 m?

The radius of the Earth is r. A satellite of mass 100 kg is at a point which is a distance 3r above the Earth's surface. What is the satellite's weight?

A CD has a diameter of 12.0 cm. If the CD is rotating at a constant frequency of 6.00 rotations per second, then the angular speed is

A circular space station (shaped like a big wheel) rotates to produce "artificial gravity". The apparent weight of an astronaut standing on the inside surface of the outer wall is equal to her weight on earth. The inside surface of the outer wall of the space station is 285 m from the axis of rotation. What is the period of rotation of the station?