To find the object's linear speed, time for one revolution, and centripetal acceleration, we can use the following formulas:
Linear speed (v): The linear speed of an object moving along a circular path can be calculated using the formula v = rω, where r is the radius of the circular path and ω (omega) is the angular velocity.
Given: Radius (r) = 5 m Angular velocity (ω) = 40 rad/s
Using the formula, we can calculate the linear speed: v = r * ω = 5 m * 40 rad/s = 200 m/s
Therefore, the object's linear speed is 200 m/s.
Time for one revolution (T): The time it takes for an object to complete one revolution along a circular path can be calculated using the formula T = 2π/ω, where ω is the angular velocity.
Given: Angular velocity (ω) = 40 rad/s
Using the formula, we can calculate the time for one revolution: T = 2π/ω = 2π/40 rad/s = π/20 s
Therefore, the time for one revolution is π/20 seconds or approximately 0.157 seconds.
Centripetal acceleration (a_c): The centripetal acceleration of an object moving along a circular path can be calculated using the formula a_c = rω^2, where r is the radius of the circular path and ω is the angular velocity.
Given: Radius (r) = 5 m Angular velocity (ω) = 40 rad/s
Using the formula, we can calculate the centripetal acceleration: a_c = r * ω^2 = 5 m * (40 rad/s)^2 = 8000 m/s^2
Therefore, the object's centripetal acceleration is 8000 m/s^2.
To summarize:
- Linear speed: 200 m/s
- Time for one revolution: π/20 seconds (approximately 0.157 seconds)
- Centripetal acceleration: 8000 m/s^2