Question

A ladybug sits 12.0 cm from the center of a Beatles music album spinning at 33.33 rpm. What is the maximum velocity of its shadow on the wall behind the turntable if illuminated parallel to the record by the parallel rays of the setting Sun?

a) (0.21 m/s)
b) (0.42 m/s)
c) (0.63 m/s)
d) (0.84 m/s)

Answer 1

The maximum velocity of the shadow on the wall behind the turntable is approximately 0.42 m/s.

Step-by-step explanation:

The maximum velocity of the shadow on the wall behind the turntable can be found using the concept of angular velocity and the relationship between linear and angular velocities. The angular velocity of the turntable can be calculated using the formula:

angular velocity (ω) = 2π × frequency

Given that the turntable is spinning at 33.33 rpm, we can convert the rpm to Hz:

frequency = 33.33 rpm × (1 min/60 s) = 0.5555 Hz

Substituting this value into the formula, we get:

angular velocity (ω) = 2π × 0.5555 Hz ≈ 3.49 rad/s

The maximum velocity of the shadow can be calculated using the formula:

maximum velocity = distance from center × angular velocity

In this case, the distance from the center is 12.0 cm, so:

maximum velocity = 12.0 cm × 3.49 rad/s = 41.88 cm/s ≈ 0.42 m/s

Therefore, the maximum velocity of its shadow on the wall behind the turntable is approximately 0.42 m/s.