Wheel A of radius ra = 14.6 cm is coupled by belt B to wheel C of radius rc = 30.2 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 5.0 rad/s2. At what time will wheel C reach a rotational speed of 52.9 rev/min, assuming the belt does not slip?

Both wheels have the same linear speed

v=ω1•r1= ω2•r2
Taking into account that
ω1=ε•t,
ω2= 2•π•n=(2•π•52.9)/60 (rad/s)
ε•t•r1=(2•π•52.9/60)•r2

t= (ω2•r2)/ε•r1=(ω2•r2)/(2•π•52.9/60)•r2 =2.29 s.

thank you!

To solve this problem, we can use the relationship between angular speed, angular acceleration, and time.

1. First, convert the rotational speed of wheel C from revolutions per minute to radians per second. Since 1 revolution is equal to 2π radians, we can use the following conversion factor:
52.9 rev/min * (2π rad/1 rev) * (1 min/60 s) = 5.528 rad/s

2. Next, we can use the equation for angular acceleration in terms of initial angular speed, final angular speed, and time:
ωf = ωi + αt
where ωf is the final angular speed (5.528 rad/s), ωi is the initial angular speed (0 rad/s), α is the angular acceleration (5.0 rad/s^2), and t is the time we need to find.

3. Rearranging the equation, we can solve for time:
t = (ωf - ωi) / α
t = (5.528 rad/s - 0 rad/s) / 5.0 rad/s^2
t = 1.1064 s

Therefore, wheel C will reach a rotational speed of 52.9 rev/min at approximately 1.1064 seconds.