Question

During the spin cycle of your clothes washer, the tub rotates at a steady angular velocity of 33.5 rad/s. Find the angular displacement of the tub during a spin of 90.7 s, expressed both in radians and in revolutions.

Answer 1

Answer: angular displacement in rad = 3038.45 rad

angular displacement in rev = 483.589 rev

Explanation: mathematically

Angular velocity = angular displacement / time taken.

Angular velocity = 33.5 rad/s, time taken = 90.7s

33.5 = angular displacement /90.7

Angular displacement = 33.5 * 90.7 = 3038.45 rad

But 1 rev =2π

Hence 3038.45 rad to rev is

3038.45/2π = 483.599 rev

Answer 2

Answer:

3038.45 in radians and

483.52 in revolutions

Explanation:

The angular velocity (ω) of a rotating body is the time (t) rate of change in the angular displacement (θ) of the body. i.e

ω = θ / t;          --------------------------(i)

The following are given in the question;

ω = 33.5rad/s

t = 90.7s

Substitute these values into equation (i) as follows;

33.5 = θ / 90.7

Solve for θ;

θ = 33.5 x 90.7

θ = 3038.45 rad

Convert the value of the displacement from radians (rad) to revolutions (rev)

Remember that;

2π rads = 1 rev

=> 3038.45 rads = (3038.45 / 2π) rev

Take π = 3.142

=> 3038.45 rads = (3038.45 / (2 x 3.142)) rev

=> 3038.45 rads = 483.52 revs

Therefore the angular displacement of the tub during a spin of 90.7s is 3038.45 in radians and 483.52 in revolutions