Question

A 0.35-kg turntable of radius 0.30 m spins about a vertical axis through its center. A constant rotational acceleration causes the turntable to accelerate from 0 to 24 revolutions per second in 8.0 s. Part A
Calculate the rotational acceleration.

\alpha = ?

Part B

Calculate the torque required to cause this acceleration.

torque = ?

Answer 1

Answer:

(a) ∝ = 18.84 rad/s^2

(b) 0.297 N m

Explanation:

m = 0.35 kg

r = 0.3 m

fo = 0 rps

f = 24 rps

t = 8 s

(A)

ωo = 2 x π x fo = 0

ω = 2 π f = 2 x 3.14 x 24 = 150.72 rad/s

Use first equation of motion for rotational motion

ω = ωo + ∝ t

Where, ∝ is the rotational acceleration

150.72 = 0 + 8 ∝

∝ = 18.84 rad/s^2

(B) Torque = Moment of inertia x rotational acceleration

Moment of inertia of turn table = 0.5 x mass x radius²  

I = 0.5 x 0.35 x 0.3 x 0.3 = 0.01575 kg m²

Torque = 0.01575 x 18.84 = 0.297 N m