Introduction This problem deals with the Coriolis force, an apparent force experienced by moving objects in a rotating frame such as the Earth. The Coriolis effect is especially significant for high-speed or long-distance movements and is calculated using the formula: Fc = 2mωv sin(φ) Where: m = mass of the object (in kg) ω = […]
Introduction This question deals with two different rotational motion concepts: (a) Rotational dynamics of the Earth to find the critical angular velocity at which objects at the equator would become weightless. (b) Coriolis force, which is an apparent force due to Earth’s rotation, affecting moving bodies in a rotating frame. Part (a): Angular Velocity for
Introduction This problem uses Kepler’s Third Law, which relates the orbital period of a satellite to the radius of its orbit. Specifically, for satellites orbiting the same planet (Saturn in this case), the square of the orbital period is proportional to the cube of the orbital radius: (T₁/T₂)² = (R₁/R₂)³ Given Data Orbital radius of
Introduction This is a classic two-dimensional collision problem involving conservation of momentum. Since the truck and car stick together after collision, it’s an example of a perfectly inelastic collision. We will use vector components to solve for the unknown initial speed of the truck and the final velocity after the collision. Given Data Mass of
Introduction This problem is based on the principle of conservation of angular momentum. When no external torque acts on a system, the total angular momentum remains constant. As the child moves toward the center, the system’s moment of inertia changes, which affects the angular velocity. Given Data Mass of child (m) = 50 kg Mass
Introduction This question is based on the principle of conservation of momentum and center of mass in a system with no external horizontal forces. Since the boat is on a lake, the system is isolated, and the center of mass of the system must remain unchanged in the absence of external forces. Given Data Mass
Introduction This is a problem involving static equilibrium. The horizontal rod is supported at one end by a hinge and at the other end by a cable inclined at an angle. To solve this, we apply the conditions of equilibrium: Sum of all horizontal forces = 0 Sum of all vertical forces = 0 Sum
Introduction This problem involves rotational motion with constant angular acceleration. We’re asked to find the angular speed, angular position, and total acceleration of a point on the rim of a rotating wheel after 2 seconds. Given Data Diameter of wheel = 2.0 m ⇒ Radius (r) = 1.0 m Angular acceleration (α) = 4.0 rad/s²
Introduction This problem deals with the effect of friction on a moving object. When a box moves across a rough surface, the frictional force does negative work, reducing the speed of the box. We’ll apply the work-energy theorem to solve the two parts of this problem. Given Data Mass of box, m = 8.0 kg
Introduction This problem involves a change in the direction of motion of a ball due to a hit by a bat. Since the direction changes from east to north, we must deal with vector quantities. The concepts of impulse and average force are used here, which are based on the impulse-momentum theorem. Given Data Mass
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