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- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/08%3A_C8)_Conservation_of_Energy-_Kinetic_and_Gravitational/8.E%3A_Potential_Energy_and_Conservation_of_Energy_(Exercises)Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) What is the change in the gravitational potential energy of the ball during th...Assume in this problem that air drag is negligible. (a) What is the kinetic energy of the ball as it leaves the hand? (b) What is the change in the gravitational potential energy of the ball during the rise to its peak? (c) If the gravitational potential energy is taken to be zero at the point where it leaves your hand, what is the gravitational potential energy when it reaches the maximum height? (d) What if the gravitational potential energy is taken to be zero at the maximum height the ball …
- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/11%3A_C11)_Rotational_Energy/11.E%3A_Fixed-Axis_Rotation_Introduction_(Exercises)An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s 2 ? (b) What is the tangential acceleration of a point 9.50 cm from the axis ...An ultracentrifuge accelerates from rest to 100,000 rpm in 2.00 min. (a) What is the average angular acceleration in rad/s 2 ? (b) What is the tangential acceleration of a point 9.50 cm from the axis of rotation? (c) What is the centripetal acceleration in m/s 2 and multiples of g of this point at full rpm? (d) What is the total distance traveled by a point 9.5 cm from the axis of rotation of the ultracentrifuge?
- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/06%3A_C6)_Conservation_of_Angular_Momentum_I/6.E%3A_Angular_Momentum_(Exercises)The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of ...The bug crawls to the center of the disk. (a) What is the new angular velocity of the disk? (b) What is the change in the kinetic energy of the system? (c) If the bug crawls back to the outer edge of the disk, what is the angular velocity of the disk then? (d) What is the new kinetic energy of the system? (e) What is the cause of the increase and decrease of kinetic energy?
- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/09%3A_C9)_Potential_Energy-_Graphs_and_Springs/9.04%3A_ExamplesInterpreting a one-dimensional potential energy diagram allows you to obtain qualitative, and some quantitative, information about the motion of a particle. For example, the negative of the slope of t...Interpreting a one-dimensional potential energy diagram allows you to obtain qualitative, and some quantitative, information about the motion of a particle. For example, the negative of the slope of the potential energy curve, for a particle, equals the one-dimensional component of the conservative force on the particle. Also, at a turning point, the potential energy equals the mechanical energy and the kinetic energy is zero, indicating that the direction of the velocity reverses there.
- https://phys.libretexts.org/Courses/Merrimack_College/Conservation_Laws_Newton's_Laws_and_Kinematics_version_2.0/08%3A_C8)_Conservation_of_Energy-_Kinetic_and_Gravitational/8.06%3A_ExamplesWe also have three velocities to worry about (or, more properly in this case, speeds, since their direction is of no concern, as long as they all point the way they are supposed to): Tarzan’s initial ...We also have three velocities to worry about (or, more properly in this case, speeds, since their direction is of no concern, as long as they all point the way they are supposed to): Tarzan’s initial velocity at the beginning of the swing, which we may call \(v_{top}\); his velocity at the bottom of the swing, just before he grabs the explorer, which we may call \(v_{bot1}\), and his velocity just after he grabs the explorer, which we may call \(v_{bot2}\). (If you find those subscripts confusi…
- https://phys.libretexts.org/Courses/Merrimack_College/Conservation_Laws_Newton's_Laws_and_Kinematics_version_2.0/03%3A_C3)_Vector_Analysis/3.02%3A__Coordinate_Systems_and_Components_of_a_Vector_(Part_2)In a plane, there are two equivalent coordinate systems. The Cartesian coordinate system is defined by unit vectors i^ and j^ along the x-axis and the y-axis, respectively. The polar coordinate system...In a plane, there are two equivalent coordinate systems. The Cartesian coordinate system is defined by unit vectors i^ and j^ along the x-axis and the y-axis, respectively. The polar coordinate system is defined by the radial unit vector r^, which gives the direction from the origin, and a unit vector t^, which is perpendicular (orthogonal) to the radial direction.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/02%3A_Math_Review/2.09%3A_Vectors/2.9.05%3A_Algebra_of_VectorsThe displacement vector \(\vec{D}_{AB}\) is the vector sum of the jogger’s displacement vector \(\vec{D}_{AT}\) along the stairs (from point A at the bottom of the stairs to point T at the top of the ...The displacement vector \(\vec{D}_{AB}\) is the vector sum of the jogger’s displacement vector \(\vec{D}_{AT}\) along the stairs (from point A at the bottom of the stairs to point T at the top of the stairs) and his displacement vector \(\vec{D}_{RB}\) on the top of the hill (from point T at the top of the stairs to the fountain at point B).
- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/06%3A_C6)_Conservation_of_Angular_Momentum_I/6.03%3A_ExamplesIn the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the ...In the absence of external torques, a system’s total angular momentum is conserved. The angular velocity is inversely proportional to the moment of inertia, so if the moment of inertia decreases, the angular velocity must increase to conserve angular momentum. Systems containing both point particles and rigid bodies can be analyzed using conservation of angular momentum. The angular momentum of all bodies in the system must be taken about a common axis.
- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/11%3A_C11)_Rotational_Energy/11.03%3A_ExamplesThe rotational kinetic energy is the kinetic energy of rotation of a rotating rigid body or system of particles. The moment of inertia for a system of point particles rotating about a fixed axis is th...The rotational kinetic energy is the kinetic energy of rotation of a rotating rigid body or system of particles. The moment of inertia for a system of point particles rotating about a fixed axis is the sum of the product between the mass of each point particle and the distance of the point particles to the rotation axis. In systems that are both rotating and translating, conservation of mechanical energy can be used if there are no nonconservative forces at work.
- https://phys.libretexts.org/Courses/Gettysburg_College/Gettysburg_College_Physics_for_Physics_Majors/05%3A_C5)_Conservation_of_Momentum/5.01%3A_Conservation_of_Linear_MomentumThe law of conservation of momentum says that the momentum of a closed system is constant in time (conserved). A closed (or isolated) system is defined to be one for which the mass remains constant, a...The law of conservation of momentum says that the momentum of a closed system is constant in time (conserved). A closed (or isolated) system is defined to be one for which the mass remains constant, and the net external force is zero. The total momentum of a system is conserved only when the system is closed.
- https://phys.libretexts.org/Courses/Georgia_State_University/GSU-TM-Introductory_Physics_II_(1112)/01%3A_Introduction_to_Physics_and_Measurements/1.06%3A_Dimensional_AnalysisFor example, if r is the radius of a cylinder and h is its height, then we write [r] = L and [h] = L to indicate the dimensions of the radius and height are both those of length, or L. Similarly, if w...For example, if r is the radius of a cylinder and h is its height, then we write [r] = L and [h] = L to indicate the dimensions of the radius and height are both those of length, or L. Similarly, if we use the symbol A for the surface area of a cylinder and V for its volume, then [A] = L 2 and [V] = L 3 . If we use the symbol m for the mass of the cylinder and \(\rho\) for the density of the material from which the cylinder is made, then [m] = M and [\(\rho\)] = ML −3 .
