Question

A ball of mass 1.0kg is moving in a circle of radius 1.0m. Calculate its acceleration if it moves with a constant angular speed of 2.0 rads-1. Suppose the ball starts from rest and moves with a constant angular acceleration of 0.02 rads-2. What is the net force on the ball 60 s after it starts moving from rest ?

Answer 1

• mass of ball(m)=0.1kg

radius of circle (r)=1.0m

angular velocity ($\omega)$ =2.0 rads^-1

angular acceleration of ball($\alpha$ )-

$\alpha$ = r$\omega^2$

= (1.0)(2²)

= 4 rads^-2

• We need to calculate angular velocity of vall after 60 sec, so

$\alpha$ = $\frac{\omega_1-\omega_2}{t}$

0.02 = $\frac{\omega_1-0}{60}$

$\omega_1$ = 1.2 rads^-1

Net Force on ball(F) = mr$\omega_1^2$

= (0.1)(1.0)(1.2²)

= 0.144 N