A top starting from rest is spun for 3 seconds achieving an angular speed of 20 rad/s. How many radians has it gone through in this time? (a is constant)
Is the answer 30 radians?
Yes. It equals
(1/2)(time)(final angular speed)
To find the number of radians the top has gone through in 3 seconds, we can use the formula for angular displacement:
θ = ω*t
where:
θ is the angular displacement (in radians)
ω is the angular speed (in radians per second)
t is the time (in seconds)
In this case, the given angular speed is 20 rad/s, and the time is 3 seconds. Substituting these values into the formula, we get:
θ = 20 rad/s * 3 s
θ = 60 radians
Therefore, the top has gone through 60 radians in 3 seconds.