# Thread: Rotational bodies

1. ## Rotational bodies

A car turns a corner with a radius of curvature of 18.2 m while braking to reduce its speed. If the brakes generate an angular deceleration of 0.7 rad/s2 what is the magnitude of the acceleration of the car half way through the corner when the car's linear speed is 4.2 m/s?

[Specify units of 'm/s2' in your answer.]

2. Originally Posted by jddery
A car turns a corner with a radius of curvature of 18.2 m while braking to reduce its speed. If the brakes generate an angular deceleration of 0.7 rad/s2 what is the magnitude of the acceleration of the car half way through the corner when the car's linear speed is 4.2 m/s?

[Specify units of 'm/s2' in your answer.]

$\displaystyle |a| = \sqrt{a_T^2 + a_c^2}$

where tangential acceleration is $\displaystyle a_T = r\alpha$

and centripetal acceleration is $\displaystyle a_c = \frac{v^2}{r}$

3. hey thanks that worked

now how did you come up with that equation? is that a defined equation in a text book?
or did you simply know that adding the tangential acceleration with the centripetal acceleration by means of Pythagorus would result in acceleration?

4. Originally Posted by jddery
hey thanks that worked

now how did you come up with that equation? is that a defined equation in a text book?
or did you simply know that adding the tangential acceleration with the centripetal acceleration by means of Pythagorus would result in acceleration?
THe car experiences 2 types of acceleration ie tangential a and centripetal a (towards the centre) . So its resultant acceleration would be the vector sum of the 2 accelerations . Phythagoras would give you the result since the 2 accelrations are 90 to each other .