Calculate Angular Acceleration & Time of Toy Car w/Vo, Vf, R, & C

[cobrasny]

1. a) A X kg toy car accelerates at constant rate from V_o m/s to V_f m/s in C revolutions while going around a circular track of radius R cm. Find:

- α, the magnitude of the angular acceleration of the car.
- t, the time it took to reach the final speed




2. To calculate the angular acceleration, I tried velocity over radius, V_o/R and V_f/R to get delta W(omega); and then tried using the formula W_f² = W_o² + 2*alpha*(C*2*Pi), and solved for alpha, but got the wrong answer. I do not know how to get time without acceleration. Any help would be appreciated.

 

[alphysicist]

Hi cobrasny,

1. a) A X kg toy car accelerates at constant rate from V_o m/s to V_f m/s in C revolutions while going around a circular track of radius R cm. Find:

- α, the magnitude of the angular acceleration of the car.
- t, the time it took to reach the final speed




2. To calculate the angular acceleration, I tried velocity over radius, V_o/R and V_f/R to get delta W(omega); and then tried using the formula W_f² = W_o² + 2*alpha*(C*2*Pi), and solved for alpha, but got the wrong answer.

What answer did you get?

 

[thomate1]

First, let's define some variables to make the calculations easier. Let C represent the number of revolutions, R represent the radius in meters, Vo represent the initial velocity in meters per second, and Vf represent the final velocity in meters per second. We can also define the angular acceleration as α and the time as t.

To find the angular acceleration, we can use the formula α = (Vf - Vo)/R. Plugging in the given values, we get:

α = (Vf - Vo)/R
α = (Vf - Vo)/(R/100) (since R is given in cm, we need to convert it to meters by dividing by 100)
α = (Vf - Vo)/(0.01*R) (since R is given in meters, we can simplify the equation)

To find the time it took to reach the final speed, we can use the formula t = C*2*Pi*R/Vf. Plugging in the given values, we get:

t = C*2*Pi*R/Vf
t = C*2*Pi*(0.01*R)/Vf (since R is given in meters, we need to convert it to cm by multiplying by 100)
t = C*0.02*Pi*R/Vf (simplifying the equation)

So the final equations are:

α = (Vf - Vo)/(0.01*R)
t = C*0.02*Pi*R/Vf

By using these equations, you should be able to calculate the angular acceleration and time for the given scenario. Remember to check your units and make sure they are consistent throughout the calculations. I hope this helps.