# A car with wheel of radius 14 inches is moving in a speed of 55 mph.Find the angular speed of the wheel in radian per sec.

your car is moving at 55 mph, which is

55*5280*12 inches/3600 seconds or

968 inches/second.

each rotation of the wheel covers 2*14*pi inches.

so the number of rotations is 968/(28pi)

or 5.5022 rotations per second

now in radians you would have 5.5022*(2pi) radians/second or

34.57 radians/second

## To find the angular speed of the wheel in radians per second, we need to convert the linear speed of the car into the number of rotations per second.

First, let's convert the car's speed from miles per hour (mph) to inches per second. There are 5280 feet in a mile, 12 inches in a foot, and 3600 seconds in an hour, so the speed in inches per second is calculated as follows:

55 mph * 5280 feet/mile * 12 inches/foot / 3600 seconds/hour = 968 inches/second.

Next, we need to determine the circumference of the wheel. The circumference of a circle is given by the formula 2 * π * radius. In this case, the radius of the wheel is given as 14 inches. So, the circumference of the wheel is:

2 * π * 14 inches = 28π inches.

Now, we can calculate the number of rotations per second by dividing the linear speed of the car (968 inches/second) by the circumference of the wheel (28π inches):

968 inches/second ÷ (28π inches) = 34.57 rotations/second.

Finally, to find the angular speed in radians per second, we multiply the number of rotations per second by 2π (since there are 2π radians in one revolution):

34.57 rotations/second * 2π radians/rotation = 69.14π radians/second, or approximately 34.57 radians/second.

Therefore, the angular speed of the wheel is approximately 34.57 radians per second.

## To find the angular speed of the wheel in radian per second, we can use the formula:

Angular speed = Linear speed / Radius

Given that the wheel has a radius of 14 inches, the linear speed of the car is 968 inches per second (as calculated earlier).

Plugging the values into the formula, we get:

Angular speed = 968 inches/second / 14 inches

Simplifying, we get:

Angular speed = 69.14 radians/second