1. An object rotates such that its angular position is given by the function: 0(t) =...

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1. An object rotates such that its angular position is given by the function: 0(t) = 30+80t-16t t is the time measured in seconds and 0 is the angle measured in degrees. a) From this expression, determine the particle's (i) angular acceleration, (ii) initial angular velocity, (iii) initial angular position. b) Determine the function for the particle's angular velocity with time. c) Determine the (i) angular position and (ii) angular velocity of the particle at t = 2s. d) Determine the time when the particle is instantaneously at rest. 2. A merry-go-round starts from rest and accelerates at rad/s for 12s. In the second regime, the merry-go-round then rotates with a constant angular velocity from t = 12s to t = 132s. After t 132s, the merry-go-round takes 18s to slow to a stop. = a) Determine the angular speed of the merry-go-round at the end of the first 12s. b) Determine the angle that the merry-go-round travelled during the first 12s. c) Determine the angle that the merry-go-round travelled during the second regime. d) Determine the angle that the merry-go-round travelled while slowing down. e) Determine the total angular displacement throughout the entire ride. f) Determine the average angular speed of the merry-go-round during the entire ride. 1. An object rotates such that its angular position is given by the function: 0(t) = 30+80t-16t t is the time measured in seconds and 0 is the angle measured in degrees. a) From this expression, determine the particle's (i) angular acceleration, (ii) initial angular velocity, (iii) initial angular position. b) Determine the function for the particle's angular velocity with time. c) Determine the (i) angular position and (ii) angular velocity of the particle at t = 2s. d) Determine the time when the particle is instantaneously at rest. 2. A merry-go-round starts from rest and accelerates at rad/s for 12s. In the second regime, the merry-go-round then rotates with a constant angular velocity from t = 12s to t = 132s. After t 132s, the merry-go-round takes 18s to slow to a stop. = a) Determine the angular speed of the merry-go-round at the end of the first 12s. b) Determine the angle that the merry-go-round travelled during the first 12s. c) Determine the angle that the merry-go-round travelled during the second regime. d) Determine the angle that the merry-go-round travelled while slowing down. e) Determine the total angular displacement throughout the entire ride. f) Determine the average angular speed of the merry-go-round during the entire ride.