Rotational Motion Practice

Question

A rotating platform makes one full rotation every 14 seconds and has a radius of 12m. If someone has a mass of 70 kg and the maximum static friction under there feet is equal to 160 N, can they stay standing on the edge of the platform.

Answer 1

Mass (m) = 70 kg

Radius (r) = 12m

Angular Velocity (w) = 2pi/14 = pi/7 radians/sec

Static Friction force (f) = 160 Newtons

Sum of the forces = -f + mrw² = -160 + (70)(12)(pi/7)² = 160 -169.2 = -9.2 Newtons

where the first force is the force holding him on the platform and the one on the right is the force trying to "sling" him off the platform in the radial direction.

It looks like the person will be fall off the platform!