Circular Motion and Gravitation

An object is moving in uniform circular motion. Which of the following statements is true about the direction of its velocity vector?

Which of the following is NOT a fundamental force?

Two objects have masses $m_1 = 10 ,\text{kg}$ and $m_2 = 20 ,\text{kg}$, and their centers are separated by a distance of $r = 2 ,\text{m}$. What is the gravitational force between them? (Use $G = 6.674 \times 10^{-11} ,\text{N} \cdot \text{m}^2/\text{kg}^2$)

If the mass of one object is doubled and the distance between two objects is also doubled, how does the gravitational force between them change?

Three identical masses ($m$) are placed at the vertices of an equilateral triangle with side length $r$. What is the magnitude of the gravitational force on one mass due to the other two?

A planet has a mass of $M = 5.97 \times 10^{24} ,\text{kg}$ and a radius of $R = 6.37 \times 10^6 ,\text{m}$. What is the approximate gravitational acceleration ($g$) on the surface of this planet? (Use $G = 6.674 \times 10^{-11} ,\text{N} \cdot \text{m}^2/\text{kg}^2$)

Which of the following statements best describes the difference between inertial and gravitational mass?

An object is moving in a circle with a radius of $r = 2 ,\text{m}$ at a constant speed of $v = 4 ,\text{m/s}$. What is the centripetal acceleration of the object?

A ball of mass $m$ is attached to a string of length $L$ and swung in a horizontal circle at a constant speed $v$. The tension in the string provides the centripetal force. If the speed of the ball is doubled, how does the tension in the string change?

A block of mass $m$ slides down an inclined plane that is rotating horizontally with angular velocity $\omega$. The coefficient of static friction between the block and the inclined plane is $\mu_s$. Derive an expression for the maximum distance $r$ from the center of rotation such that the block does not slide down the plane.