Answer to Question #90095 in Mechanics | Relativity for Awesome

Question

A ball of radius 5.5cm rolls down an inclined plane from rest. if its angular velocity 5 seconds later is 8.5 rad/s. calculate a. its angular acceleration b. its linear velocity after 5 seconds

Answer 1

a. Angular acceleration is the rate of change angular velocity, so for time t = 5s and angular velocity w = 8.5rad/s the answer is .

$$\alpha = \frac{\omega}{t} = \frac{8.5}{5}=1.7rad/s^2.$$

b. The relation between the angular velocity and the linear velocity is

$$v = \omega*R,$$

where w - the angular velocity, R - the radius of the ball. Using this formula we obtain v = 8.5*5.5 = 46.75cm/s or 0.4675 m/s.