Formulas worth remembering

Question 1

Roller coaster (top of motion)

At the Top of the Loop: At the top of a vertical loop, gravity and the normal force both contribute to the centripetal force required to keep the roller coaster on the circular path.

Answer 1

Question 2

Roller coaster (top of motion)
minium speed to make the loop

Answer 2

Question 3

Roller coaster** (bottom of the loop)**

At the Bottom of the Loop: At the bottom of the loop, the normal force acts in the opposite direction to gravity, contributing to the centripetal force.

Answer 3

Question 4

Cars on Banked Corners (Without Friction)

n the case of a car rounding a banked curve without friction, the banking angle θ. This provides the necessary centripetal force to keep the car on the curve without slipping.

Answer 4

Question 5

Cars on Banked Corners (With Friction)

When friction is present, it contributes to the centripetal force along with the normal force. The velocity of the car can then vary depending on whether it is below or above the ideal speed:

Answer 5

Question 6

Cars on Flat Roads (With Friction)

On a flat, unbanked road, friction is the only source of centripetal force. The maximum velocity the car can safely maintain without slipping is determined by the frictional force:

Answer 6

Question 7

Orbital Velocity of a statelite

Orbital velocity refers to the speed a satellite (or any object) needs to maintain a stable orbit around a planet or star. It’s derived from the balance between gravitational force and the centripetal force needed to keep the object in orbit.

Answer 7

Remember it is **independant **of the mass of the statelite

Question 8

Escape Velocity

Escape velocity is the minimum speed required for an object to break free from a planet or star’s gravitational pull without any further propulsion.

Answer 8

Remember it is **independant **of the mass of the object being launched.

Question 9

Electron Gun Velocity Formula

An electron gun accelerates electrons by applying a voltage difference, which converts electrical potential energy into kinetic energy. The velocity of the electron can be derived using energy conservation principles:

Answer 9

This formula comes from equating the kinetic energy
to the electric potential energy
𝑒V. eV gained as the electron moves through the potential difference.