Imagine that a rigid body having a moment of inertia I rolls down an inclined sl
ID: 2242024 • Letter: I
Question
Imagine that a rigid body having a moment of inertia I rolls down an inclined slope at an ange beta (without slipping).
i. From equation a=mgsin(x)/(I/R^2 +m) derive the translational accerelation of the rigid body using algebra
ii. Draw a graph for the acceleration a ranging from I=0 to I=mR^2.
iii. Which object among slid cylinder, hollow cylinder, sphere and hollw sphere woulld take the longest or shortest time to reach the lowest point of the inclined slope if each object is released at the same position on the slope? Why? Assume each rigid body has the same mass m and radius R.
iv. If we assume I=0, what physical meaning des the acceleration a have?
Explanation / Answer
i)
ii)
source: www[dot]wolframalpha[dot]com
iii)
A rigid body with a smaller moment of inertial will have a greater acceleration and shortest time to reach the lowest point... therefore the solid sphere will have the longest time because it have the smaller moment of inertia.
iv)
if I=0, therefore a=m g sin(theta), and the object can be treated as a point.