Explain why an object in circular motion at constant speed is accelerating, and solve for the linear velocity of an object given mass, frequency, and radius, and also solve for gravitational potential

Mass $m = 450 \text{ g} = 0.45 \text{ kg}$
Frequency $f = 3 \text{ revolutions/second}$
Radius $r = 1.5 \text{ m}$

The formula for angular velocity is $\omega = 2\pi f$.

The formula for linear velocity is $v = \omega r$.

The linear velocity is $\boxed{\text{28.27 m/s}}$.

2.

Mass $m = 0.05 \text{ kg}$
Compression distance $x = 0.2 \text{ m}$
Spring constant $k = 15 \text{ N/m}$

The elastic potential energy stored in the compressed spring is converted into gravitational potential energy when the ball reaches its maximum height.
Elastic potential energy $PE_s = \frac{1}{2}kx^2$
Gravitational potential energy $PE_g = mgh$
Equating the two: $PE_s = PE_g$

The maximum height reached is $\boxed{\text{0.61 m}}$.

3. To show a reading of $3.62 \text{ cm}$ on a vernier caliper:

• The zero mark of the vernier scale should be placed just past the $3.6 \text{ cm}$ mark on the main scale.
• The second mark (2) on the vernier scale should be aligned exactly with any mark on the main scale. This assumes a least count of $0.01 \text{ cm}$ for the vernier caliper.