# Rotational motion and tangential speed?

• yramos9
In summary, a 919 kg rollercoaster is about to go up a hill that acts as the top of a circle with a diameter of 16.21m. The question asks for the maximum speed the coaster can have without leaving the track. To solve this, one can use force balance and a free-body diagram to find the required centripetal force. This should be equal to the force of gravity at the point where the coaster does not fly off. The answer can be found by using the equation F=ma and solving for the maximum tangential velocity. This problem may be part of an 11th grade physics course.
yramos9

## Homework Statement

A 919 kg rollercoaster is about to go up a hill that acts as the top of a circle 16.21m in diameter. What is the fastest that car can move (in m/s) without leaving a track?
known:
mass: 919 kg
diameter: 16.21
radius: 8.105

## Homework Equations

Vt=r$$\omega$$
$$\omega$$=$$\theta$$/time

## The Attempt at a Solution

i have no idea how to work this out without knowing the time or speed or somekind of time measurement. Is there another way to solve this?

centrifugal force

force balance

free body diagram

huh??

Draw a free-body diagram of the cart with centrifugal force pulling it up and gravity pulling it down. The sum of the forces on the cart should be zero in the radial direction (since that's the direction for which you don't want motion). Centrifugal force should be a function of tangential velocity, which is the velocity in question.

What level of physics is this? Gravity would realistically be a function of the angle about the center of the circle and only be exactly g when the cart is exactly on the tip of the half-circle. But you could probably neglect this if it's an introductory physics course.

this is 11th grage physics pre-ap.. i don't think I've learned what youre trying to teach me.

When gravity can provide the centripetal acceleration required to keep the roller coaster on the track, the coaster doesn't fly off. Otherwise, it does. When does gravity exactly equal the required centripetal force? (Hint: F=ma)

## 1. What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. It is different from linear motion, which is movement in a straight line.

## 2. How is tangential speed related to rotational motion?

Tangential speed is the speed at which an object moves along a circular path. It is directly related to rotational motion because an object's tangential speed is determined by its rotational speed and the radius of its circular path.

## 3. What is the difference between tangential speed and angular velocity?

Tangential speed is the linear speed at which an object moves along a circular path, while angular velocity is the rate at which an object rotates around an axis. They are related by the formula tangential speed = angular velocity x radius.

## 4. How does rotational inertia affect rotational motion?

Rotational inertia is the resistance of an object to changes in its rotational motion. Objects with a larger rotational inertia require more force to change their rotational speed or direction, while objects with a smaller rotational inertia can change their rotational motion more easily.

## 5. What are some real-life examples of rotational motion and tangential speed?

Some examples of rotational motion and tangential speed include the rotation of a bicycle wheel, the spinning of a top, and the movement of a Ferris wheel. These objects all rotate around an axis or center point, and their tangential speed determines how fast they move along their circular path.

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