A stone attached to the end of an inelastic string is whirled round insc a circular path of radius20cm if the stone makes15% complete revolution in 5sec calculate it s angular and linear velocity within this period
15% complete revolution in 5sec
Huh? Please proofread
Va = 15rev/5s * 6.28rad/rev = 18.84 rad/s.
C = 2pi*r = 6.28*20cm = 125.6 cm = circumference.
V = 15rev/5s * 125.6cm/rev = ----cm/s.
To calculate the angular and linear velocity of the stone, we first need to know the formula for angular velocity.
The formula for angular velocity is:
Angular velocity (ω) = θ / t
Where:
- θ is the angle covered (in radians)
- t is the time taken
Given that the stone makes a 15% complete revolution, we can calculate the angle covered by multiplying 15% by the full angle of a circle.
θ = 15/100 * 2π radians
Next, we need to calculate the time taken for the stone to make this 15% complete revolution, which is given as 5 seconds.
Now we can substitute the values into the formula to find the angular velocity:
Angular velocity (ω) = (15/100 * 2π) radians / 5 seconds
Simplify the equation:
Angular velocity (ω) = (3/20 * π) radians / 1 second
To calculate the linear velocity, we need to know the relation between angular velocity and linear velocity in a circular motion.
The formula for linear velocity (v) in terms of angular velocity (ω) is:
Linear velocity (v) = ω * r
Where:
- ω is the angular velocity (in radians per second)
- r is the radius of the circular path (in meters)
The radius of the circular path is given as 20 cm, which is equivalent to 0.2 meters.
Now we can substitute the values into the formula to find the linear velocity:
Linear velocity (v) = (3/20 * π) radians / 1 second * 0.2 meters
Simplify the equation:
Linear velocity (v) = (3/100 * π) meters / 1 second
Therefore, the angular velocity of the stone is (3/20 * π) radians per second, and the linear velocity is (3/100 * π) meters per second.
To calculate the angular and linear velocity of the stone, we need to understand a few concepts first.
Angular velocity (ω) is defined as the rate at which an object rotates around a central point, expressed in radians per second (rad/s). It represents the change in angle over time.
Linear velocity (v) is the speed at which an object moves along a circular path, expressed in meters per second (m/s). It represents the linear distance traveled per unit time.
Given:
Radius of circular path (r): 20 cm (0.2 m)
Time to complete 15% revolution (t): 5 seconds
First, let's calculate the angle covered by the stone during the given time period:
15% of a complete revolution is 0.15 * 2π radians, where 2π represents a complete revolution (360 degrees).
Angle (θ) = 0.15 * 2π radians
Next, we can calculate the angular velocity using the formula:
ω = θ / t
Substituting the values, we get:
Angular velocity (ω) = (0.15 * 2π radians) / 5 seconds
Now, let's calculate the linear velocity using the formula:
v = ω * r
Substituting the values, we get:
Linear velocity (v) = (0.15 * 2π radians / 5 seconds) * 0.2 meters
To obtain the final answer, simplify the expression:
Angular velocity (ω) ≈ 0.1885 rad/s
Linear velocity (v) ≈ 0.3769 m/s
Therefore, within the given period of 5 seconds, the angular velocity of the stone is approximately 0.1885 radians per second, and the linear velocity is approximately 0.3769 meters per second.