Wheel A of radius ra = 13.9 cm is coupled by belt B to wheel C of radius rc = 34.3 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 5.7 rad/s2. At what time will wheel C reach a rotational speed of 168.2 rev/min, assuming the belt does not slip?
so for c: v = w*r = 168.2*0.343m =57.6926
and therefore for a: w = v/r = 57.6926/0.139m = 415.055
is that correct?
and for the acceleration:
for a: a= 5.7*0.139 = 0.7923
and for c: 0.7923/0.343 = 2.3099
but how do I get time ??
Your calculations look OK except:
(1) w has to be in radians per second, not rpm.
(2) You need to include dimensions with the numbers.
For example v is in m/s and a is in m/s^2. For the time required, divide the final angular velocity of C by its angular acceleration rate, 5.7 rad/s^2. .
To find the time it takes for wheel C to reach a rotational speed of 168.2 rev/min, assuming constant acceleration, you can use the formula for angular acceleration:
ω = ω₀ + αt
where:
ω is the final angular speed of wheel C (in rad/s)
ω₀ is the initial angular speed of wheel C (which is 0 since it starts from rest)
α is the angular acceleration of wheel C (which can be obtained from the acceleration of wheel A)
t is the time we want to find
First, let's convert 168.2 rev/min into rad/s:
ω = (168.2 rev/min) * (2π rad/rev) * (1 min/60 s) ≈ 17.65 rad/s
Now, let's substitute the values into the equation:
17.65 rad/s = 0 + 2.3099 rad/s^2 * t
To solve for t, rearrange the equation:
t = (17.65 rad/s) / (2.3099 rad/s^2) ≈ 7.6363 s
So, it will take approximately 7.6363 seconds for wheel C to reach a rotational speed of 168.2 rev/min, assuming the belt does not slip.