The take-up reel of a cassette tape has an average radius of 1.5 cm. find the length of tape (in meters) that passes around the reel in 19 s when the reel rotates at an average angular speed of 4.5 rad/s.

 1.28 m

Explanation:

Given;

Radius, r = 1.5 cm =  0.015 m

Time, t = 19 s

Average angular speed = 4.5 rad/s

Consider a point when the tape is moving at a constant velocity along the circumference of the circular reel of radius  r. The linear velocity  v at this point is given by;

                                      v = rω                           (1)

Where

v is the linear velocity of the circular motion

r is the radius of the reel

ω is the the angular velocity.

At a point the tap undergoes a linear motion before passing round the reel of the cassette. The linear velocity v at this point is given by;

                                v = L/t                          (2)

where;

v is the velocity of the linear motion

L is the length of the tape (distance covered by the tape)

t is the time taken

Equating equation(1) and equation (2)

                       L/t = rω

                       L = rωt

Substituting the given values,

                       L = 0.015 × 4.5 × 19

                       L = 1.2825 m

                       L = 1.28 m

the area between the graph and the t axis