A large merry-go-round rotates at one revolution each 8.5 s. When shut off, it decelerates uniformly to a stop in 15 s.
A) What is the angular acceleration in rad/s^2
B) How many revolutions does the merry-go-round make during the deceleration in rev?
A) What is the angular acceleration in rad/s^2
B) How many revolutions does the merry-go-round make during the deceleration in rev?
-
Convert one revolution each 8.5 s to rad/s.
one revolution each 8.5 s * (2*pi rad/1 revolution)
A) Use the angular kinematic formula
Wf = Wi + alpha*t
where Wf = 0, Wi = "one revolution each 8.5 s" converted to rad/s, and t = 15 s.
B) 2 ways to do that
1-Since the acceleration is uniform, the average angular velocity is
Wave = (Wf+Wi)/2
and then Wave = total angular displacement / time. Solve for total angular displacement. The units will be rad, so convert back to revolutions
(result in rad) * (1 rev/(2*pi rad)
one revolution each 8.5 s * (2*pi rad/1 revolution)
A) Use the angular kinematic formula
Wf = Wi + alpha*t
where Wf = 0, Wi = "one revolution each 8.5 s" converted to rad/s, and t = 15 s.
B) 2 ways to do that
1-Since the acceleration is uniform, the average angular velocity is
Wave = (Wf+Wi)/2
and then Wave = total angular displacement / time. Solve for total angular displacement. The units will be rad, so convert back to revolutions
(result in rad) * (1 rev/(2*pi rad)