the earthis moving around the sun in a circular orbit of radius 1.5*10^11. it makes one revolution per year.find the angular speed of earth in radian/sec, and the tangential speed of earth using the formula v=r.w , and tangetial speed ?

angular speed in radians/sec

w = (2 pi radians)/(# of seconds in 1 year)

Once you have w, you can compute the tangential speed with the formula given. You have given value of r but you did not say if the number is km or meters.

To find the angular speed of the Earth in radians per second, we need to determine the angle it covers in one revolution (one year).

1 revolution = 2π radians

Since the Earth makes one revolution per year, its angular speed can be calculated as follows:

Angular speed = (2π radians) / (1 year)

However, it's important to convert the time unit from years to seconds to match the angular speed unit. There are 365 days in a year and 24 hours in a day, so we have:

Angular speed = (2π radians) / (1 year) * (365 days / 1 year) * (24 hours / 1 day) * (3600 seconds / 1 hour)

Simplifying the units, we have:

Angular speed = (2π radians) / (1 year) * (365 * 24 * 3600 seconds)

Now, let's calculate it:

Angular speed = (2 * 3.14) / (1) * (365 * 24 * 3600) radians/second

The resulting value will give us the angular speed of the Earth in radian/second.

To find the tangential speed of the Earth, we can use the formula v = r * ω, where v is the tangential speed, r is the radius, and ω is the angular speed.

In this case, the radius of the Earth's orbit is 1.5 * 10^11 meters, and we just calculated the angular speed in radian/second. Let's substitute these values in:

Tangential speed = (1.5 * 10^11 meters) * (angular speed in radian/second)

Calculating this will give us the tangential speed of the Earth.