A small rubber wheel is used to drive alarge pottery wheel. The two wheels are m

Question

   A small rubber wheel is used to drive alarge pottery wheel. The two wheels are mounted so that theircircular edges touch. The small wheel has a radius of 3.5cmand accelerates at the rate of 8.5 rad/s, and it is in contact withthe pottery wheel (radius 23.5cm) without slipping. Calculate: A) The angular acceleration of the pottery wheel B) The time it takes the pottery wheel to reach itsrequired speed of 72 rpm Please show all steps    A small rubber wheel is used to drive alarge pottery wheel. The two wheels are mounted so that theircircular edges touch. The small wheel has a radius of 3.5cmand accelerates at the rate of 8.5 rad/s, and it is in contact withthe pottery wheel (radius 23.5cm) without slipping. Calculate: A) The angular acceleration of the pottery wheel B) The time it takes the pottery wheel to reach itsrequired speed of 72 rpm Please show all steps

Explanation / Answer

The radius of the small wheel is r = 3.5 cm = 3.5 *10-2 m The small wheel accelerates at the rate of 8.5 rad/s The radius of the pottery wheel is R = 23.5 cm = 23.5 *10-2 m A)The speed of the small wheel is v = r * w Here,w = 8.5 rad/s or v = 3.5 * 10-2 * 8.5 = 0.2975 m/s The time taken by the small pottery wheel to rotate withangular speed of 8.5 rad/s is v = u + gt Here,u = 0 m/s and g = 9.8 m/s2 or t = (v/g) or t = (0.2975/9.8) = 0.03s The angular acceleration of the small pottery wheel is w = wo + t Here,wo= 0 rad/s or = (w/t) or = (8.5/0.03) = 283.3 rad/s2 B)The required speed of the pottery wheel is w = 72 rpm = 72 * (2/60) = 7.536 rad/s The time taken by the pottery wheel to reach its requiredspeed of 72 rpm is w = wo + t Here,wo= 0 rad/s and = 283.3rad/s2 or w = t or t = (w/) = (7.536/283.3) = 0.027s or w = t or t = (w/) = (7.536/283.3) = 0.027s

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