Calculate the linear acceleration of a car

[nautica]

a) Calculate the linear acceleration of a car, the 0.300 m radius tires of which have an angular acceleration of 10 rad/sec^2, assume no slippage.

a = ?
r = 0.30 m
Rot acc = 10.0 rad/s^2

a = r * (rotational acc)
a = .3 m * 10 rad/s^2
a = 3.0 m/s^2

b) How many revolutions do the tires make in 2.5 s if they start from a rest?

V final = 10 rad/s^2 * 2.5 s * 1 rev / 2pie rad = 3.98 rev/s

(Vf - Vo)/2 should give average velocity so

(3.98 rev/s)/2 = 1.98 rev/s

1.98 rev/s * 2.5 s = 4.97 rev

c) What is their final angular velocity?

W = Wo + (rotational acc) * time

W = 10 rad/s^2 = 25 rad/s

d) What is the final velocity of the car?

v = (.3m) * (25 rad/s) = 7.5 m/s

Could someone check this please - I feel relatively confident - but you will not hurt my feelings if you tell me I am wrong.

Thanks
Nautica

 

[jamesrc]

Your answers are correct. You could have done part b in one step if you used Δθ = ωo*t + .5*α*t^2 and there was a typo in the third line of your solution to part c, but that's neither here nor there.

 

[nautica]

I see that now

Thanks
Nautica