Question

A 33 1/3 rpm record on a turntable uniformly reaches its operating speed in 2.45 seconds once it is turn on. a) What is the angular distance traveled during this time? b) If a dime located on the turntable slides out after it has been switched on, what is the coefficient of static friction between the record and the dime?

Answer 1

Answer:

a) 4.28 rad

b) μ = ω²r / g

Explanation:

(a) Given:

ω₀ = 0 rad/s

ω = 33⅓ rpm × (2π rad/rev) × (1 min / 60 s) = 3.49 rad/s

t = 2.45 s

Find: Δθ

Δθ = ½ (ω + ω₀) t

Δθ = ½ (3.49 rad/s + 0 rad/s) (2.45 s)

Δθ = 4.28 rad

(b) Draw a free body diagram of the dime. There are 3 forces:

Weight force mg pulling down,

Normal force N pushing up,

Friction force Nμ pushing towards the center.

Sum of forces in the y direction:

∑F = ma

N − mg = 0

N = mg

Sum of forces in the centripetal direction:

∑F = ma

Nμ = m v²/r

mgμ = m ω²r

μ = ω²r / g