In a fairground ride a child of mass 37 kg stands against the inside surface of a circular cylinder of radius 3.9m that rotates around its vertical axis of symmetry. The cylinder has an angular speed of 1.3 rad/s and an angular acceleration of 0.12 rad s^-2. What is the radial inward force on the child.
M*R*w^2
w is the angular speed
M is the mass
R is the radius
The angular acceleration doesn't matter in the radial direction.
To find the radial inward force on the child, we need to consider the centripetal force acting on the child due to the circular motion.
The formula for centripetal force is given by:
F = m * a
Where F is the centripetal force, m is the mass of the object, and a is the centripetal acceleration.
The centripetal acceleration can be calculated using the formula:
a = r * ω^2
Where a is the centripetal acceleration, r is the radius of the circular motion, and ω is the angular speed.
First, let's calculate the centripetal acceleration:
a = (3.9m) * (1.3 rad/s)^2
= 3.9 m * 1.69 rad^2/s^2
= 6.591 m/s^2
Now, we can calculate the centripetal force:
F = (37 kg) * (6.591 m/s^2)
= 243.867 N
Therefore, the radial inward force on the child is approximately 243.867 Newtons.