Exam 5: Circular Motion

A 5,000 kg satellite is orbiting the Earth in a circular path. The height of the satellite above the surface of the Earth is $800 \mathrm{~km}$ . The angular speed of the satellite as it orbits the Earth is $\left(\mathrm{M}_{\mathrm{E}}=5.98 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37\right.$ $\times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}$ )

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.00 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.00 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.00 \mathrm{rad} / \mathrm{sec}$ for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the magnitude of the (total) acceleration of a point $4.00 \mathrm{~cm}$ from the center at the time 10.0 seconds from the start?

A $5,000 \mathrm{~kg}$ satellite is orbiting the Earth in a geostationary orbit. The height of the satellite above the surface of the Earth is $\left(\mathrm{M}_{\mathrm{E}}=5.98 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

A $4.00 \mathrm{~kg}$ mass is moving in a circular path of radius $2.50 \mathrm{~m}$ with a constant angular speed of $5.00 \mathrm{rad} / \mathrm{sec}$ . The magnitude of the radial force on the mass is

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 10.0 seconds from the start?

Two planets travel in circular orbits about a star at radii of $r_{a}=2 R$ and $r_{b}=R$ , respectively. What is the ratio of their periods $\mathrm{T}_{\mathrm{a}} / \mathrm{T}_{\mathrm{b}}$ ?

A $2.00 \mathrm{~kg}$ mass is moving in a circular path with a radius of $5.00 \mathrm{~cm}$ . The mass starts from rest and, with constant angular acceleration, obtains an angular velocity of $6.00 \mathrm{rad} / \mathrm{sec}$ in $3.00 \mathrm{sec}$ . The mass then comes to a stop with constant angular acceleration in $4.00 \mathrm{sec}$ . The radial component of acceleration of the mass at $2.00 \mathrm{sec}$ is

A $2.0 \mathrm{~kg}$ mass is moving in a circular path with a radius of $5.00 \mathrm{~cm}$ . The mass starts from rest and, with constant angular acceleration, obtains an angular velocity of $6.00 \mathrm{rad} / \mathrm{sec}$ in $3.00 \mathrm{sec}$ . The mass then comes to a stop with constant angular acceleration in $4.00 \mathrm{sec}$ . The radial component of acceleration of the mass at $5.00 \mathrm{sec}$ after the start is

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The CD continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the linear speed of a point $4.0 \mathrm{~cm}$ from the center at the time 25.0 seconds from the start?

A 4,000 kg satellite is traveling in a circular orbit $200 \mathrm{~km}$ 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? $\left(\mathrm{M}_{\mathrm{E}}=5.98 \times 10^{24} \mathrm{~kg}, \mathrm{R}_{\mathrm{E}}=6.37 \times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.0 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.0 \mathrm{rad} / \mathrm{sec}$ . The $\mathrm{CD}$ continues rotating at $5.0 \mathrm{rad} / \mathrm{sec}$ 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 $4.0 \mathrm{~cm}$ from the center at the time 15.0 seconds from the start?

A $2.60 \mathrm{~kg}$ mass is moving in a circular path with a constant angular speed of $5.50 \mathrm{rad} / \mathrm{sec}$ and with a linear speed of $3.50 \mathrm{~m} / \mathrm{s}$ . The magnitude of the radial force on the mass is

An object is moving in a circular path of radius $4.00 \mathrm{~m}$ . If the object moves through an angle of 30.0 degrees, then the tangential distance traveled by the object is

At what distance from the center of the Earth would one's weight be one third of that recorded on the Earth's surface? Let the Earth's radius be $\mathrm{R}$ .

A 4,000 kg satellite is traveling in a circular orbit $200 \mathrm{~km}$ 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? $\left(M_{E}=5.98 \times 10^{24} \mathrm{~kg}, R_{E}=6.37 \times 10^{6} \mathrm{~m}, \mathrm{G}=6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\right)$

An airplane is traveling at $250 \mathrm{~m} / \mathrm{s}$ in level flight. In order to make a change in direction, the airplane travels in a horizontal curved path. To fly in the curved path, the pilot banks the airplane at an angle such that the lift has a horizontal component that provides the horizontal radial acceleration to move in a horizontal circular path. If the airplane is banked at an angle of 15.0 degrees, then the radius of curvature of the curved path of the airplane is

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

An airplane is traveling at $150 \mathrm{~m} / \mathrm{s}$ in level flight. In order to make a change in direction, the airplane travels in a horizontal curved path. To fly in the curved path, the pilot banks the airplane at an angle such that the lift has a horizontal component that provides the horizontal radial acceleration to move in a horizontal circular path. If the airplane is banked at an angle of 12.0 degrees, then the radius of curvature of the curved path of the airplane is

$\mathrm{A} C D$ has a diameter of $12.0 \mathrm{~cm}$ . If the $\mathrm{CD}$ is rotating at a constant frequency of 4.00 rotations per second, then the linear speed of a point on the circumference is

A CD with a diameter of $12.0 \mathrm{~cm}$ starts from rest and with a constant angular acceleration of $1.00 \mathrm{rad} / \mathrm{sec}^{2}$ acquires an angular velocity of $5.00 \mathrm{rad} / \mathrm{sec}$ . The $\mathrm{CD}$ continues rotating at $5.00 \mathrm{rad} / \mathrm{sec}$ for 15.0 seconds and then slows to a stop in 12.0 second with a constant angular acceleration. What is the angular distance traveled by a point $4.00 \mathrm{~cm}$ from the center, at the time 25.0 seconds from the start?