- #1

- 109

- 0

## Homework Statement

A laboratory apparatus consists of a low friction, low mass turntable which carries a large, flat, round, solid disk. The disk is 10.0 inches or 25.4 cm in diameter and has a mass of 4.34 kg. The turntable base turns on a cylinder 1 7/8 inches (4.76 cm) in diameter. A string is wrapped around the base cylinder (hub) of the turntable. The string passes over pulley of negligible friction and mass to a hanging mass of 200 g. The hanging mass is released from rest and falls 80.0 cm in 7.05 s. (a) What is the acceleration of the falling mass assuming constant acceleration? (b) What is the angular acceleration of the turntable? Through how many radians does the turntable turn in the 7.05 seconds? How many revolutions is this? What is the angular velocity and the tangential velocity of an object attached to the edge of the large disk at the end of the 7.05 s?

## Homework Equations

## The Attempt at a Solution

Well I'll write down every variable I have

DISK:

Diameter = 25.4cm

Mass = 4.34 kg

CYLINDER:

Diameter = 4.76 cm

HANGING MASS:

200 kg

Velocity_i = 0

Δy = 80.0cm

Time = 7.05s

(a) What is the acceleration of the falling mass assuming constant acceleration?

So for this, knowing that acceleration is constant and this is a linear acceleration I can use

Δy = v_i * t + 1/2 * a * t²

we want a so

a = 2(Δy - (v_i * t)) / t²

0

a = 2Δy / t²

a = 2(.80m) / 7.05s² = .032m/s²

(b) What is the angular acceleration of the turntable? Through how many radians does the turntable turn in the 7.05 seconds? How many revolutions is this? What is the angular velocity and the tangential velocity of an object attached to the edge of the large disk at the end of the 7.05 s?

This is where I get stuck...I know that I can use

ω = ω_o + α * t

Δθ = ω_o * t + 1/2 * α * t²

ω² = ω_o ² + 2 * α * t²

I mean I can rearrange each one for α

α = (ω - ω_o) / t

α = 2(Δθ - (ω_o * t)) / t²

α = (ω² - ω_o²) / 2t²

But I don't know the final angular velocity, nor the Δθ because I don't know how many times it will spin.

Can anyone give me a hint here?