May the Torque Be With You
What force keeps an object moving in a circular path?
Centripetal force
What happens to the required centripetal force if the mass of an object doubles but speed and radius stay the same?
It doubles
Which of Kepler’s laws states that planets sweep out equal areas in equal times?
Kepler’s Second Law
What happens to the gravitational force between two objects if the distance between them doubles?
It decreases by a factor of 4.
Why do astronauts in the ISS appear weightless?
They are in free fall, constantly falling around Earth.
A car moves in a circle with a radius of 50 m at a speed of 20 m/s. What is its centripetal acceleration?
8 m/s2
A 2 kg ball is whirled in a circle of radius 1.5 m at 4 m/s. What is the centripetal force?
Fc = 21.3 N
If a planet is twice as far from the Sun, how much longer will it take to orbit?
Period increases by a factor of approx. 2.83
Find the gravitational force between two 10 kg masses separated by 1 meter.
F = 6.674*10-9 N
How much force does Earth exert on a 75 kg astronaut in orbit 400 km above Earth’s surface?
F = 651 N
If a car moves in a circle at a constant speed, does it accelerate? Explain why.
Yes, because the direction of velocity is constantly changing, which means there is acceleration.
Why do you feel pressed against the door in a turning car even though there’s no outward force acting on you?
It's inertia (AGAIN)! Your body wants to continue moving in a straight line while the car turns.
What does Kepler’s First Law say about planetary orbits?
Planets orbit the Sun in elliptical paths, with the Sun at one focus.
If Earth were twice as massive but had the same radius, how would gravity change?
It would double.
What is the relationship between a planet’s orbital radius and its tangential speed?
v is proportional to one over the square root of the orbital radius. Further out you go, the slower you move.
A satellite orbits Earth at a radius of 7000 km. If its velocity is 7.5 km/s, what is its orbital period in seconds? In hours?
T = 5.86*103 seconds
T = 1.63 hours
A 500 kg satellite orbits a planet at 8,000 m/s in a circular path of radius 6.0 × 10⁶ m. Find the gravitational force acting on it.
Fc = 5.33*103 N
A planet orbits a star at an average distance of of 3 AU (distance between the earth and its sun). How long is its orbital period in Earth years?
T = 5.2 Earth years
A 1000 kg satellite orbits Earth at an altitude equal to Earth’s radius. What is the gravitational force acting on it?
F = 9.8*103 N
A geostationary satellite orbits at 35,786 km above Earth. What is its velocity?
v = 3.07*103 m/s
If centripetal force is always directed toward the center, why do people in a rotating carnival ride feel like they are being pushed outward?
It’s an illusion caused by inertia (DARN YOU NEWTON!!!!!)! Your body wants to move in a straight line, but the wall of the ride applies a force that keeps you moving in a circle. This is often mistaken for an “outward” force.
The Moon orbits Earth in a nearly circular orbit of radius 3.84 × 10⁸ m. Given Earth's mass is 5.97 × 10²⁴ kg, find the Moon’s acceleration toward Earth.
ac = 2.72*10-3 m/s2
An exoplanet orbits a distant star at an average distance of 3.0 × 10¹¹ m with an orbital period of 2.5 years. Using Newton's version of Kepler’s third law, determine the mass of the star.
M = 2.57*1030 kg, about twice the mass of OUR sun!
Two stars of equal mass orbit their common center of mass at a distance of 5 × 10¹¹ m from each other. If each star’s mass is 2 × 10³⁰ kg, find the gravitational force between them.
F = 1.07*1027 N
A rotating space station must simulate Earth’s gravity at a radius of 150 m. What is its required angular velocity?
w = 2.57*10-1 rad/s