A car has wheels with a 13 inch radius. If each wheel's rate of turn is 6 revolutions per second, find the angular speed in units of radians/second.

Angular speed tails that how fast a object resolves. The angular acceleration is radians/second.

To find the angular speed of the wheel, we need to know about the angular speed.

Angular speed is the rate of change of angle with respect to time of an object. Angular speed tails that how fast a object resolves.

It can be given as,

Here, is the linear velocity and is the radius.

Given information-

The radius of the wheels of the car is 13 inch.

The revolutions per second of the each wheel is 6 rpm.

As the wheel rotates at 6 revolutions per seconds. Thus its linear velocity is 6 rev/sec. The one rev/sec equals to the rad.

Thus the linear velocity is,

Put the values in the above formula,

Hence the angular acceleration is radians/second.

Learn more about the angular speed here;
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Step-by-step explanation:

The expression for calculating the angular speed is expressed as

w = v/r

v is the linear speed

r is the radius

Given

v = 6rev/s

r = 13in

since 1rev = 2πrad

6rev = 12πrad

v = 12πrad/s

Substitute;

w = 12π/13

w = 12π/13 rad/seconds