A particle of mass 1.6 x 10-27 kg is revolving on a circular path of radius 10cm under the
Influence of a centripetal force of 2.5 x 10-12. Find out the angular velocity?
I don't know if you've learned this equation:
F = m r w^2
where F=centripetal force, w = angular velocity
Assuming the force is in Newtons (you don't show the units), be sure to covert r = 10 cm to 0.1 m before solving.
To find the angular velocity, we can use the formula:
Angular velocity (ω) = v / r
Where:
v = linear velocity
r = radius
To find the linear velocity, we can use the equation:
Centripetal force (F) = m * v^2 / r
Where:
m = mass
v = linear velocity
r = radius
Given:
Mass (m) = 1.6 x 10^-27 kg
Centripetal force (F) = 2.5 x 10^-12 N
Radius (r) = 10 cm = 0.1 m
Let's calculate the linear velocity first:
2.5 x 10^-12 N = (1.6 x 10^-27 kg) * v^2 / 0.1 m
Rearranging the equation:
v^2 = (2.5 x 10^-12 N * 0.1 m) / (1.6 x 10^-27 kg)
v^2 = 0.15625 x 10^-12 kg.m / 1.6 x 10^-27 kg
v^2 ≈ 0.09765625 x 10^15 m^2/s^2
Taking the square root of both sides:
v ≈ √(0.09765625 x 10^15 m^2/s^2)
v ≈ 9.84375 x 10^6 m/s
Now, we can calculate the angular velocity:
ω = v / r
ω = (9.84375 x 10^6 m/s) / (0.1 m)
ω = 9.84375 x 10^7 rad/s
Therefore, the angular velocity is approximately 9.84375 x 10^7 rad/s.
To find the angular velocity, we need to use the formula:
Angular velocity (ω) = v / r
Where v is the linear velocity and r is the radius of the circular path.
To find the linear velocity, we can use the formula:
Centripetal force (F) = (m * v^2) / r
Rearrange the formula to solve for v:
v = √(F * r / m)
Now, plug in the given values:
m = 1.6 x 10^-27 kg (mass of the particle)
r = 10 cm = 0.1 m (radius of the circular path)
F = 2.5 x 10^-12 N (centripetal force)
Calculate the linear velocity (v):
v = √((2.5 x 10^-12 N * 0.1 m) / (1.6 x 10^-27 kg))
v = 4.9087 x 10^7 m/s (approximately)
Finally, substitute the value of v into the formula for angular velocity:
ω = 4.9087 x 10^7 m/s / 0.1 m
ω = 4.9087 x 10^8 rad/s (approximately)
Therefore, the angular velocity is 4.9087 x 10^8 rad/s.