A STONE WHIRED AT THE END OF A ROPE 30CM LONG, MAKE 10 COMPLETE REVOLUTION IN 2 SECONDS. FIND A. AUGULAR VELOCITY IN RADIANS PER SECOND B.THE LINEAR SPEED C.THE DISTANCE IN 5 SECONDS
10 times 2 pi radians / 2 seconds = 10 pi
v = omega r = 10 pi * 0.30 meters/second
or answer to a times 0.30 meters
distance v * t = 10 pi * 0.30 * 5
or answer to b times 5 seconds
A. V = 10rev./2s * 6.28rad/rev. = 31.4 rad/s.
B. Circumference =2 pi * r = 6.28 * 0.30 = 1.884 m.
V = 10rev./2s * 1.884m/rev. =
C. d = V * t = V * 5 =
Use value of V calculated in B.
I don't know, how do you get the answer
anonymous is right, keep it up
To find the angular velocity, we need to first find the total angle covered in 2 seconds when the stone makes 10 complete revolutions.
1. Calculate the total angle covered by the stone in 2 seconds:
- In 1 second, the stone makes 10/2 = 5 complete revolutions.
- In each revolution, the angle covered is 360 degrees, or 2π radians.
- Therefore, in 2 seconds, the total angle covered is 5 x 2π = 10π radians.
2. Calculate the angular velocity:
- Angular velocity is defined as the change in angle per unit time.
- In this case, the angular velocity is the total angle covered in 2 seconds divided by the time taken, which is 2 seconds.
- So, the angular velocity is 10π radians / 2 seconds = 5π radians per second. (Answer: A)
Now, let's move on to finding the linear speed and the distance covered in 5 seconds.
3. Calculate the linear speed:
- Linear speed is the distance traveled per unit time.
- In this case, the distance traveled is the circumference of the circle formed by the stone at the end of the rope, which is 2π times the radius.
- The radius is given as 30 cm, so the circumference is 2π x 30 cm = 60π cm.
- To find the linear speed, we divide the distance traveled by the time taken, which is 2 seconds.
- Therefore, the linear speed is 60π cm / 2 seconds = 30π cm/s. (Answer: B)
4. Calculate the distance covered in 5 seconds:
- Now that we know the linear speed, we can calculate the distance traveled in 5 seconds.
- The distance traveled in 5 seconds is the linear speed multiplied by the time taken, which is 30π cm/s x 5 seconds = 150π cm. (Answer: C)
So, the answers are:
A. Angular velocity = 5π radians per second
B. Linear speed = 30π cm/s
C. Distance traveled in 5 seconds = 150π cm