Awheel with radius 32 cm is rotating at a rate of 14 rev/sa wheel with radius 32 cm is rotating at a rate of 14 rev/s(a) what is the angular speed in radians per second? (b) in a time interval of 5 s, what is the angle in radians through which the wheel rotates? (c) at t=10 s the angular speed begins to increase at a rate of 1.3 rad/s/s. at t=15 s, what is the angular speed in radians per second?

(a) 88.0 rad/s

The angular speed of the wheel is

Keeping in mind that

1 revolution = radians

The angular speed in radians/second can be found by solving the proportion:

From which we find

(b) 440 radians

Assuming the wheel is rotating at constant angular speed, the angular displacement of the wheel at time t is given by

where

is the angular speed

t is the time

Substituting

t = 5 s

we find the angle through which the wheel has rotated after 5 seconds:

(c) 94.5 rad/s

The angular speed after a time t is given by

where

is the angular speed at t=10 s, when the acceleration starts

is the angular acceleration

The duration of the acceleration is

t = 15 s - 10 s = 5 s

So substituting this value into the equation, we find the new angular speed:

can be answered using momentum.

momentum = p

p1= mass1 * velocity1

p1 = p2

therefore

p1 = 6kg * 4m/s

p1 = 24kgm/s

p2=m2 * v2

24 kgm/s = 7kg * v2

v2 = 24 kgm/s / 7kg

v2= 3.42 m/s