Final answer:
The angle generated by point P after 8 seconds on the circle is π/6 radians when it rotates with an angular speed of π/12 radians per second.
Step-by-step explanation:
To find the angle generated by point P in 8 seconds on a circle with a radius of 60 cm and a rotating ray OP with an angular speed of π/12 radians per second, we use the formula for angular displacement, which is θ = ωt, where θ is the angle in radians, ω (omega) is the angular speed, and t is the time in seconds.
Given that ω = π/12 radians per second and t = 8 seconds, we can calculate θ as follows:
θ = (π/12 rad/s) × 8 s = (π/6) rad = π/6 radians.
Therefore, the angle generated by point P after 8 seconds is π/6 radians.
To find the angle generated by point P in 8 seconds, we need to multiply the angular speed by the time:
θ = ωt
θ = (π/12 rad/s)(8 s)
θ = π/3 radians
Therefore, the angle generated by point P in 8 seconds is π/3 radians.