Simple Rolling Motion Calculations | Velocity and Acceleration

In summary, the car is traveling at 75 km/h on a level road in the positive direction of an x axis. The velocity of the car is 20.83 m/s at the center of each tire for both the woman and hitchhiker. The velocity at the top of each tire is 41.7 m/s for the hitchhiker and 20.8 m/s for the woman. The velocity at the bottom of each tire is 0 m/s for both the woman and hitchhiker. The magnitude of the acceleration is 0 m/s^2 at the center of each tire for both the woman and hitchhiker. The magnitude of the acceleration at the top of each tire is 723 m/s^
  • #1
mbrmbrg
496
2

Homework Statement



A car travels at 75 km/h on a level road in the positive direction of an x axis. Each tire has a diameter of 60 cm.
Relative to a woman riding in the car, what are the following values?

(a) the velocity v at the center of each tire [0 m/s]
(b) the velocity v at the top of each tire [20.8 m/s]
(c) the velocity v at the bottom of each tire [-20.8 m/s]
(d) the magnitude a of the acceleration at the center of each tire [0 m/s^2]
(e) the magnitude a of the acceleration at the top of each tire [? m/s^2]
(f) the magnitude a of the acceleration at the bottom of each tire [? m/s^2]

Relative to a hitchhiker sitting next to the road, what are the following values?
(g) the velocity v at the center of each tire [20.83 m/s]
(h) the velocity v at the top of each tire [41.7 m/s]
(i) the velocity v at the bottom of each tire [0 m/s]
(j) the magnitude a of the acceleration at the center of each tire [0 m/s]
(k) the magnitude a of the acceleration at the top of each tire
(l) the magnitude a of the acceleration at the bottom of each tire



Homework Equations



1km/h=0.27778m/s
1m=100cm
[tex]a_c=\frac{v^2}{r}[/tex]

The Attempt at a Solution



This is a relative motion problem: relative to the woman the wheels are rotating; relative to the hitchiker, the wheels are rolling.
I solved most of the problem, and gave my [correct] answers in brackets.

For the acceleration at the top and bottom of the wheel (parts e,f,k,&l):
First off, since both the woman and the hichiker are in inertial frames of reference, they will observe the same acceleration.
Secondly, since the woman sees the wheels as rotating, the acceleration at their rim is centripetal acceleration, and so
[tex]a=a_c=\frac{v^2}{r}=\frac{(20.83m/s)^2}{0.6m}=723m/s^2[/tex]
As you probably assumed from the fact that I'm posting, this is INCORRECT (as are the answers 0, -723, and 721).

PS cool new format to force work to be shown... I think.
 
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  • #2
Nice work. I think the only error is using the diameter 0.6m as the radius in your angular acceleration calculation.

And thanks for the positive comment on the Homework Posting Template. Yeah, when it gets used, it's a huge help to us.
 
  • #3
thank you! and here I sit, insisting that I cannot understant torque, etc...
(derogitory term) stupid errors.
 

1. What is simple conceptual rolling?

Simple conceptual rolling is a scientific concept that refers to the movement of an object over a surface without any external forces acting on it except for the force of gravity. This type of rolling is often used in physics experiments and is a simplified version of real-world rolling.

2. How is simple conceptual rolling different from real-world rolling?

In simple conceptual rolling, we assume that there is no friction or other external forces acting on the object, whereas in real-world rolling, there are always some external forces present that affect the movement of the object. Simple conceptual rolling is used to simplify and understand the basic principles of motion without the complications of real-world factors.

3. What are the key factors that affect simple conceptual rolling?

The key factors that affect simple conceptual rolling are the mass and shape of the object, the angle of the surface it is rolling on, and the force of gravity. These factors determine the speed and direction of the rolling object.

4. How is simple conceptual rolling used in scientific experiments?

Simple conceptual rolling is often used in physics experiments to study the principles of motion and to make predictions about the movement of objects. By simplifying the factors that affect rolling, scientists can better understand and manipulate the variables to observe and analyze the motion of an object.

5. Can simple conceptual rolling be applied to real-world scenarios?

While simple conceptual rolling is a simplified version of real-world rolling, it can still be applied to some real-world scenarios. For example, it can be used to predict the motion of a ball rolling down a ramp or the movement of a wheel on a flat surface. However, in most real-world situations, there are other factors, such as friction and air resistance, that need to be considered for more accurate predictions.

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