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Table of Rotational Inertia Values
Table of Rotational Inertia Values
Sliding v. Rolling without slipping - NOTES DIAGRAM
We have seen that the center of gravity of different objects (Sliding, solid disk, hoop, solid sphere, hollow sphere) all accelerate down a ramp at different rates (acceleration of center of mass).
We will now explore the quantitative support of these findings.
What is causing the object to rotate (source of torque)?
What is the net force (ΣF) acting parallel to the ramp? (mgsinθ)
What is the net torque (Στ) causing the object to rotate? (Ff x r)
What is the link between rotational acceleration and linear acceleration? (a=rα)
Race to the Bottom
Race to the Bottom
Five objects, all with the same mass M and made of the same material, are released on an inclined ramp with a vertical height H. The ramp is long enough that all objects can reach the bottom. The objects are:
A frictionless block: This object can only slide down the ramp without any rotation.
A solid sphere: This object rolls without slipping down the ramp.
A solid cylinder: This object rolls without slipping down the ramp.
A thin-walled hollow cylinder (hoop): This object rolls without slipping down the ramp.
A hollow sphere: This object rolls without slipping down the ramp.
All the rolling objects have the same outer diameter D.
The Problem:
The frictionless block is released from rest at a position of x along the ramp as measured from the bottom. It takes a time tslide to reach the bottom of the ramp.
From what positions along the ramp (measured as the distance x from the bottom) should each of the other four objects be released from rest so that they all arrive at the bottom of the ramp at the same time tslide?
Translational Acceleration in Terms of Rotational Acceleration.
Translational Acceleration in Terms of Rotational Acceleration.
The mass hanger and mass will fall at a rate less than the acceleration due to gravity. In terms of the variables listed below, determine acceleration of the mass hanger.
On the following diagram, label the positions of the following variables:
Mass 1 (m1)
Radius 1 (r1)
Radius 2 (r2)
Mass 2 (m2)
Angular Acceleration (𝛼)
Translational Acceleration (a)
Paper Towel Drop
Paper Towel Drop
Two rolls of paper towels are dropped at the same time. We hold on to the paper of one and let it unroll (Unrolling Roll A). If we release the falling roll (B) from a height of 1.5 m, from what height should we drop the unrolling roll so they hit at the same time?
Support your prediction with the appropriate measurements and calculations.
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