Question

In: Physics

a. Calculate the linear acceleration (in m/s2) of a car, the 0.340 m radius tires of...

a. Calculate the linear acceleration (in m/s²) of a car, the 0.340 m radius tires of which have an angular acceleration of 11.0 rad/s². Assume no slippage.

b. How many revolutions do the tires make in 2.50 s if they start from rest?

c. What is their final angular velocity (in rad/s)?

d. What is the final velocity (in m/s) of the car?

Expert Solution

a.

Linear acceleration or tangential acceleration = a_t = Angular acceleration () * radius (r)

a_t = * r = 11 * 0.34 = 3.74 m/s^2

b.
Let t = 2.5s be time taken
Formula :- = t + 1/2 t^2

Angle rotated ( ) = 0.t + 1/2 * * t^2 = 1/2 * 11 * 2.5^2 = 34.375 rad

2 rad = 1 revolution
34.375 rad = 1/ 2 * 34.375 rev = 54

So , number of revolutions = 54

c.
Final angular velocity

= 0 + 11* 2.5
= 27.5 rad/s

d.

= 27.5 rad/s * 0.34 m = 9.35 m/s

genius_generous answered 12 hours ago

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