Q: Two spheres of mass $$10\ \text{kg}$$ and $$25\ \text{kg}$$ are positioned $$5\ \text{m}$$ apart. Where should a third sphere be placed so the net gravitational force on it is zero?

$$3.57\ \text{m}$$\ from\ the\ 10\ \text{kg}\ sphere$

Q: Three 50-kg masses are arranged in an equilateral triangle with side length 0.6 m. What is the magnitude of the net gravitational force on the bottom mass?

$$2.6 \times 10$$^{-8}$$\ \text{N}$$

Question 1

A car tire of radius 0.40 m rotates 10,000 times while driving. How far did the car travel?

Accepted Answer

$$4,000\ 	ext{m}$$

Question 2

An object moves a total distance of 1,000 m around a circle of radius 30 m. How many degrees does the object go through?

Accepted Answer

$$1,910$$^{\circ}$$

Question 3

A wheel of radius 5 m accelerates from 60 RPM to 180 RPM in 2 s. What is its angular acceleration?

Accepted Answer

$$10\pi\ 	ext{rad/s}^2$$

Question 4

A disc of radius 10 m rotates at 180 RPM. What is the linear speed at a point 7 m from the center?

Accepted Answer

$$132\pi\ 	ext{m/s}$$

Question 5

A carousel of radius 10 m completes one cycle every 45 s. What is the radial (centripetal) acceleration of a person at the edge?

Accepted Answer

$$0.195\ 	ext{m/s}^2$$

Question 6

A satellite orbits Earth at a speed of $$7,670\ 	ext{m/s} in a $$nearly circular orbit. What is its orbital altitude above Earth's surface? (Earth's radius $$R_E = 6.37 	imes 10^6$\ 	ext{m}$$, $$M_E = 5.97 	imes 10$$^{24}$$\ 	ext{kg})$$

Accepted Answer

$$4.0 	imes 10^5$\ 	ext{m}$$

Question 7

What is the minimum speed required for a baseball to orbit a spherical asteroid of mass $$7 	imes 10$$^{16}$$\ 	ext{kg}$$ and diameter $$22\ 	ext{km}$$?

Accepted Answer

$$6.5\ 	ext{m/s}$$

Question 8

Two spheres of mass $$10\ 	ext{kg}$$ and $$25\ 	ext{kg}$$ are positioned $$5\ 	ext{m}$$ apart. Where should a third sphere be placed so the net gravitational force on it is zero?

Accepted Answer

$$3.57\ 	ext{m}$$\ from\ the\ 10\ 	ext{kg}\ sphere$

Question 9

A small 3 kg block is tied to the end of a 2 m string and slides around in a circle on a frictionless table, completing a rotation every 4 seconds. What is the tension in the string?

Accepted Answer

$$7.4\ 	ext{N}$$

Question 10

A satellite in geosynchronous orbit around Earth has an orbital period equal to Earth's rotation. What is the height of this orbit above Earth's surface? ($$M_E = 5.97 	imes 10$$^{24}$$\ 	ext{kg}$$, $$R_E = 6.37 	imes 10^6$\ 	ext{m}$$, $$T = 24\ 	ext{hr})$$

Accepted Answer

$$3.6 	imes 10^7$\ 	ext{m}$$

Question 11

A wheel of radius 0.30 m rolls without slipping along a flat surface at 10 m/s. What is the angular speed of the wheel?

Accepted Answer

$$33.3\ 	ext{rad/s}$$

Question 12

A planet has mass $$6 	imes 10$$^{24}$$\ 	ext{kg}$$ and surface gravity $$7\ 	ext{m/s}^2. $$What is its radius?

Accepted Answer

$$7.4 	imes 10^6$\ 	ext{m}$$

Question 13

A 0.50-kg ball is tied to the end of a 4 m cord and spins in a horizontal plane at constant speed, with the cord making a $$30^{\circ}$$ angle with the vertical. What is the speed of the ball?

Accepted Answer

$$4.9\ 	ext{m/s}$$

Question 14

What is the equation for the orbital speed of a satellite in a circular orbit around a planet of mass $$M$$ and orbital radius $$r$$?

Accepted Answer

$$v_{sat} = \sqrt{\frac{GM}{r}}$$

Question 15

Three 50-kg masses are arranged in an equilateral triangle with side length 0.6 m. What is the magnitude of the net gravitational force on the bottom mass?

Accepted Answer

$$2.6 	imes 10$$^{-8}$$\ 	ext{N}$$

Question 16

A satellite orbits the Moon with a period of 2 hours. What is its orbital altitude? ($$M_{Moon} = 7.35 	imes 10$$^{22}$$\ 	ext{kg}$$, $$R_{Moon} = 1.74 	imes 10^6$\ 	ext{m})$$

Accepted Answer

$$1.1 	imes 10^6$\ 	ext{m}$$

Question 17

What is the equation for the gravitational force between two point masses $$m_1$$ and $$m_2$$ separated by distance $$r$$?

Accepted Answer

$$F_G = \frac{G m_1$ m_2$}{r^2$}$$

Circular Motion, Orbits, and Gravity – Study Notes

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