a particle is completing 5 revolution per second in a circle of radius 6 cm.calculate its linear velocity and the centripetal acceleration acting on it.
change 5 rev to 10PI rad
w=10PI rad/sec
velocity=w*radius
centripetal acceleartion= w^2 * r
C = 6.28*r = 6.28 * 6cm = 37.68cm/rev.
V = 5rev/s * 37.68cm/rev = 188.4cm/rev = Linear velocity.
To calculate the linear velocity of the particle completing 5 revolutions per second in a circle of radius 6 cm, you can use the formula:
Linear velocity = (circumference of the circle) x (number of revolutions per second)
The circumference of a circle can be calculated using the formula:
Circumference = 2πr
where r is the radius of the circle.
Let's calculate the linear velocity first:
Circumference = 2π(6 cm) = 12π cm ≈ 37.68 cm
Linear velocity = (37.68 cm) x (5 revolutions per second)
Therefore, the linear velocity of the particle is 188.4 cm/s.
To calculate the centripetal acceleration, we can use the formula:
Centripetal acceleration = (linear velocity)^2 / radius
Let's calculate the centripetal acceleration:
Centripetal acceleration = (188.4 cm/s)^2 / 6 cm
Centripetal acceleration = (35445.6 cm^2/s^2) / 6 cm
Therefore, the centripetal acceleration acting on the particle is approximately 5907.6 cm^2/s^2.
To calculate the linear velocity and centripetal acceleration of a particle completing revolutions per second in a circle of radius cm, we can use the following formulas:
1. Linear velocity (v) can be calculated using the formula:
v = 2πr/T
where π is approximately 3.14, r is the radius of the circle, and T is the time taken to complete one revolution.
2. Centripetal acceleration (a_c) can be calculated using the formula:
a_c = (v^2)/r
where v is the linear velocity and r is the radius of the circle.
Let's calculate both the linear velocity and centripetal acceleration step by step.
Given:
Number of revolutions per second = 5
Radius (r) = 6 cm
Step 1: Calculate the time taken to complete one revolution (T).
In this case, since the particle is completing 5 revolutions per second, the time taken for one revolution (T) would be 1/5 seconds.
So, T = 1/5 seconds.
Step 2: Calculate the linear velocity (v).
Using the formula v = 2πr/T, we can substitute the given values:
v = (2 * 3.14 * 6 cm) / (1/5 seconds)
v = (37.68 cm) / (0.2 seconds)
v = 188.4 cm/s
Therefore, the linear velocity of the particle is 188.4 cm/s.
Step 3: Calculate the centripetal acceleration (a_c).
Using the formula a_c = (v^2)/r, we can substitute the given values:
a_c = (188.4 cm/s)^2 / 6 cm
a_c = 35494.56 cm^2/s^2 / 6 cm
a_c = 5915.76 cm/s^2
Therefore, the centripetal acceleration acting on the particle is 5915.76 cm/s^2.