A stone whirled at the end of a rope 30cm long makes 10 revolution in 2 seconds.find;(I) the angular velocity in radians per second,(II) the linear speed,(III) the distance covered in 5 seconds.
Pls you guys should help me out,i can't solve this question.
it take 0.2 seconds to go 2 pi = 6.28 radians so 6.28 / 0.2 radians/second
distance = angular velocity * R * t = (6.28/0.2) * 0.30 * 5
To find the answers to these questions, we'll need to use some basic formulas related to circular motion and angular velocity.
(I) The angular velocity is defined as the change in angle divided by the change in time. In this case, the stone makes 10 revolutions in 2 seconds, so we can calculate the angular velocity using the formula:
Angular velocity = (2 * π * number of revolutions) / time
Angular velocity = (2 * π * 10) / 2 = 31.42 radians per second
Therefore, the angular velocity is 31.42 radians per second.
(II) The linear speed is the distance traveled per unit of time. It is calculated by multiplying the radius of the circle (which is the length of the rope) with the angular velocity. The formula is:
Linear speed = radius * angular velocity
Linear speed = 30 cm * 31.42 radians per second
To convert cm to meters, we divide it by 100:
Linear speed = (30/100) meters * 31.42 radians per second
Linear speed = 0.3 meters * 31.42 radians per second
Linear speed = 9.426 meters per second
Therefore, the linear speed is 9.426 meters per second.
(III) To find the distance covered in 5 seconds, we need to know the circumference of the circular path that the stone follows. The circumference of a circle is calculated by multiplying the diameter of the circle (which is twice the radius) with π. So, the formula is:
Distance = circumference of the circle * number of revolutions
In this case, the radius is 30 cm, so the diameter is 60 cm.
Again, we convert cm to meters by dividing it by 100:
Diameter = 60 cm / 100 = 0.6 meters
Therefore, the circumference of the circle is:
Circumference = 0.6 meters * π
Number of revolutions = 10
Distance = 0.6 meters * π * 10
Distance = 18.85 meters
Therefore, the distance covered in 5 seconds is 18.85 meters.
To summarize:
(I) The angular velocity is 31.42 radians per second.
(II) The linear speed is 9.426 meters per second.
(III) The distance covered in 5 seconds is 18.85 meters.