Circular and Projectile Motion, Work, and Energy Concepts

• These study notes cover concepts related to circular motion, projectile motion, work, and energy.

Circular Motion

• When a ladybug is on a spinning merry-go-round, it is more likely to fly off as the speed increases because the friction force is insufficient to provide the necessary centripetal acceleration at high speeds.
• When a race car travels around a circular track at a constant speed, its kinetic energy is constant.
• If a string hanging from a rearview mirror angles away from the vertical by 10° while driving at constant speed around a curve with a 200-meter radius, the speed is approximately 20 m/s.
• The magnitude of a pumpkin's acceleration on a Ferris wheel rotating at a constant speed is constant and equal to $v^2/R$, where $v$ is the speed of the pumpkin and $R$ is the radius of the wheel. It can also be described as equal to $R \omega^{2}$, where $R$ is the radius and $\omega$ is the angular velocity.
• When a car makes a sharp left turn and a passenger is pressed against the passenger-side door, the most accurate statement is that the door is exerting an inward (centripetal) force.

Velocity

• The velocity of a car is given by $\vec{v} = 6.0 \mathrm{~m} / \mathrm{s} \hat{i} - 4.0 \mathrm{~m} / \mathrm{s} \hat{j}$, therefore the car's speed is calculated to be 7.2 m/s .

Projectile Motion

• When a package is released from an airplane flying at a constant altitude and horizontal velocity, and air resistance is negligible, the package will remain vertically under the plane.
• A golf ball is launched at a 20° degree above the horizontal with an initial speed of 50 m/s. Assuming air resistance is negligible, the speed at the highest point is $(50 \mathrm{~m} / \mathrm{s}) \cdot \cos \left(20^{\circ}\right)$.

Work

• When a box is being pushed across a horizontal surface at constant speed with an applied horizontal force, the amount of work done by friction as the box moves through a displacement $\Delta x$ is given by $-\mu_{k} F_{\mathrm{N}} \Delta x$.
• If a person does an amount of work $W$ to stretch a spring by an amount of $\Delta x$, then the work required to stretch the same spring by an amount of $2 \Delta x$ is $4W$.
• While a crate is given an initial shove and is slowed to a stop by friction, negative work is done on the crate by friction.

Power

• When a motor lifts an object of mass $m$ at constant speed $v$, the average power delivered by the motor is $mgv$.
• When a 1200 kg car traveling at 20 m/s skids to a halt with a coefficient of friction of 0.90, the skid distance is approximately 25.2 meters before stopping.
• When a 10 kg bucket is lowered at a constant speed of 2.0 m/s by a rope as the bucket descends 10 m, the work done by the tension in the rope on the bucket is -980 Joules.

Study notes covering circular motion principles such as centripetal acceleration and kinetic energy in circular paths. Also covers projectile motion. Includes concepts of work and energy.