A small rubber wheel (rotating CCW) is used to drive a large pottery wheel start
ID: 2265534 • Letter: A
Question
A small rubber wheel (rotating CCW) is used to drive a large
pottery wheel starting from rest and rotating CW. They are
mounted as shown in the diagram, so that their circular edges touch.
The small wheel has a radius of 2.0 cm and accelerates at the rate of
7.2 rad/s2
. It is in contact with the pottery wheel (radius 25.0 cm)
without slipping.
(a) Calculate the angular acceleration of the pottery wheel. Explain your reasoning.
(b) Calculate the time it takes the pottery wheel to reach its required speed of 65 rpm.
(c) How many revolutions does the small wheel make in this time?
A small rubber wheel (rotating CCW) is used to drive a large pottery wheel starting from rest and rotating CW. They are mounted as shown in the diagram, so that their circular edges touch. The small wheel has a radius of 2.0 cm and accelerates at the rate of 7.2 rad/s2 . It is in contact with the pottery wheel (radius 25.0 cm) without slipping. Calculate the angular acceleration of the pottery wheel. Explain your reasoning. Calculate the time it takes the pottery wheel to reach its required speed of 65 rpm. How many revolutions does the small wheel make in this time?Explanation / Answer
a)
tangential acceleration for both wheels is same
a_tan = r1*alfa1 = 0.02*7.2 = 0.144 m/s^2
angular acceleration of pottery wheel,
alfa2 = a_tan/r2 = 0.144/0.25 = 0.576 rad/s^2
b)
w1 = 0
w2 = 65 rpm = 65*2*pi/60 = 6.8 rad/s
w2 = w1 + alfa2*t
6.8 = 0 + 0.576*t
t = 6.8/0.576 = 11.8 s
c)
theta1 = w1*t + 0.5*alfa1*t^2
= 0 + 0.5*7.2*11.8^2
= 502.23 radians
= 79.97 revolutions
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