The road wheel of a motor vehicle increases speed uniformly from 50 rev/min to 1100 rev/min in 40 seconds.calculate the angular acceleration of the wheel in rad/seconds squared,if the diameter of the wheel is 0.7 meters what is the linear acceleration of a point on a Tyre trend.

Vo = 50rev/min * 1min/60s * 6.28rad/rev = 5.23 rad/s.

V = 1100rev/min * 1min/60s * 6.28rad/rev = 115.1 rad/s.

a. V = Vo + a*t = 115.1.
5.23 + a*40 = 115.1,
a = 2.75 rad/s^2.

b. Circumference = pi * Dia. = 3.14 * 0.7 = 2.2 m.
Linear acceleration = 2.75rad/s^2 * 1rev/6.28rad * 2.2m/rev =

angular acceleration= change in anglevelocity/time=(1100-50)2PI/60)/40 rad/sec

linear tangential acceleration= angularAccelerationabove*radius

What is the answer of the linear acceleration

To calculate the angular acceleration of the wheel, we can use the following formula:

Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / Time

Given:
Initial angular velocity (ω1) = 50 rev/min
Final angular velocity (ω2) = 1100 rev/min
Time (t) = 40 seconds

First, we need to convert the initial and final angular velocities from rev/min to rad/s. Since 1 revolution is equal to 2π radians, we can use the conversion factor:

1 revolution = 2π radians

Converting the initial angular velocity:
ω1 = 50 rev/min = 50 * 2π radians/1 min * 1 min/60 s = (π/3) radians/s

Converting the final angular velocity:
ω2 = 1100 rev/min = 1100 * 2π radians/1 min * 1 min/60 s = (11π/3) radians/s

Now, we can substitute the values into the formula to calculate the angular acceleration:

α = (ω2 - ω1) / t
= ((11π/3) - (π/3)) / 40
= (10π/3) / 40
= 10π / 120
= π / 12
≈ 0.2618 rad/s²

Therefore, the angular acceleration of the wheel is approximately 0.2618 rad/s².

To find the linear acceleration of a point on the tire's tread, we need to relate it to the angular acceleration. The linear acceleration (a) of a point on the tire's tread is related to the angular acceleration (α) and the radius (r) by the formula:

a = α * r

Given:
Diameter (d) = 0.7 meters

Since the diameter is given, we can calculate the radius (r) by dividing the diameter by 2:

r = d/2 = 0.7/2 = 0.35 meters

Substituting the values of α and r into the formula:

a = (π / 12) * 0.35
= π / 12 * 0.35
= 0.0915 m/s²

Therefore, the linear acceleration of a point on the tire's tread is approximately 0.0915 m/s².