An object moves in the xy plane such that x = R cos ωt and y = R sin ωt. Here x and y are the coordinates of the object, t is the time, and R and ω are constants. (a) Eliminate t between these equations to find the equation of the curve in which the object moves. What is this curve? What is the meaning of the constant ω? (b) Differentiate the equations for x and y with respect to the time to find the x and y components of the velocity of the body, vx and vy. Combine vx and vy to find the magnitude and direction of v. Describe the motion of the object, (c) Diferentiate vx and vy with respect to the time to obtain the magnitude and direction of the resultant acceleration.
An object moves in the xy plane such that x = R cos ωt and y = R sin ωt. Here x and y are the coordinates of the object, t is the time, and R and ω are constants. (a) Eliminate t between these equations to find the equation of the curve in which the object moves. What is this curve? What is the meaning of the constant ω? (b) Differentiate the equations for x and y with respect to the time to find the x and y components of the velocity of the body, vx and vy. Combine vx and vy to find the magnitude and direction of v. Describe the motion of the object, (c) Diferentiate vx and vy with respect to the time to obtain the magnitude and direction of the resultant acceleration.
Amit Saxena , 10 Years ago
Grade upto college level
