Final answer:
To calculate the tangential speed and acceleration of a spinning wheel, one must convert the given angular velocity into radians per second, use the formula for tangential speed (Vt = rω), and find angular acceleration to then calculate tangential acceleration (at = rα).
Step-by-step explanation:
A wheel having a radius of 20 cm starts from rest and rotates with an angular velocity of 60 rev/min in 10 sec. To find the tangential speed and tangential acceleration we must first convert units where appropriate and then use the relevant physics equations.
Tangential Speed (Vt)
First, let's convert the angular velocity from revolutions per minute to radians per second:
(60 rev/min) × (2π rad/rev) × (1 min/60 s) = 6π rad/s
The tangential speed, Vt, can be found using the formula Vt = rω, where r is the radius and ω is the angular velocity.
Tangential Acceleration (at)
We would use the formula at = rα to calculate tangential acceleration, where α is the angular acceleration. To find α, we use the formula α = (ω - ω0)/t because the wheel started from rest (ω0 = 0), so α = (6π rad/s) / 10s = 0.6π rad/s². Substituting the values in, we get at = (0.2 m) × (0.6π rad/s²).