Part A) A girl ties a toy airplane to the end of a string and swings it around her head. The plane’s average angular speed is 2.1 rad/s. In what time interval will the plane move through an angular displacement of 3.9 rad? Answer in units of s. Part B) A horizontal disk with a radius of 7.8 m rotates about a vertical axis through its center. The disk starts from rest and has a constant angular acceleration of 5.9 rad/s 2 . At what value of t will the radial and tangential components of the linear acceleration of a point on the rim of the disk be equal in magnitude? Answer in units of s. Solution here, A) angular speed, w = 2.1 rad/s angular displcement , theta = 3.9 rad time taken , t = theta /w t = 3.9 / 2.1 s = 1.86 s B) r = 7.8 m angular accelration ,alpha = 5.9 rad/s^2 at time t the radial accelration = tangential accelration alpha * r = w^2 * r alpha = ( alpha * t)^2 5.9 = (5.9 * t)^2 t = 0.41 the time taken is 0.41 s .

1. Part A) A girl ties a toy airplane to the end of a string and swings it around her head. The
plane’s average angular speed is 2.1 rad/s. In what time interval will the plane move through
an angular displacement of 3.9 rad? Answer in units of s.
Part B) A horizontal disk with a radius of 7.8 m rotates about a vertical axis through its center.
The disk starts from rest and has a constant angular acceleration of 5.9 rad/s 2 . At what value of
t will the radial and tangential components of the linear acceleration of a point on the rim of the
disk be equal in magnitude? Answer in units of s.
Solution
here,
A)
angular speed, w = 2.1 rad/s
angular displcement , theta = 3.9 rad
time taken , t = theta /w
t = 3.9 / 2.1 s = 1.86 s
B)
r = 7.8 m
angular accelration ,alpha = 5.9 rad/s^2
at time t
the radial accelration = tangential accelration
alpha * r = w^2 * r
alpha = ( alpha * t)^2

2. 5.9 = (5.9 * t)^2
t = 0.41
the time taken is 0.41 s