Answer to Question #305832 in Mechanics | Relativity for Quân Jason

Question

A string is wrapped around a solid disk of radius R that sits on a frictionless incline with angle theta as shown. The string is pulled up the plane with Tension T in such a way that it unwinds without slipping from the disk and the disk rolls without slipping down the incline. What is the linear acceleration (a) of the the disk down the plane.

Please help. Thank you

Answer 1

Explanations & Calculations

• Since the tension force is readily given you can apply Newton's second law to the disk upwards the incline to get the linear acceleration.

$\qquad\qquad \begin{aligned} \small F&=\small ma\\ \small T-mg\sin\theta&=\small ma\\ \small a&=\small \frac{T-mg\sin\theta}{m} \end{aligned}$