A Classical Approach of Newtonian Mechanics

8 ROTATIONAL MOTION 8.11 Combined translational and rotational motion

Worked example 8.6: Horsepower of engine

Question: A car engine develops a torque of τ = 500 N m and rotates at 3000 rev./min..

What horsepower does the engine generate? ( 1 hp = 746 W).

Answer: The angular speed of the engine is

ω = 3000 × 2 π/60 = 314.12 rad./s.

Thus, the power output of the engine is

P = ω τ = 314.12 × 500 = 1.57 × 105 W.

In units of horsepower, this becomes

1.57 × 105

(^) P =
746
= 210.5 hp.
Worked example 8.7: Rotating cylinder
Question: A uniform cylinder of radius b = 0.25 m is given an angular speed
of ω 0 = 35 rad./s about an axis, parallel to its length, which passes through its
centre. The cylinder is gently lowered onto a horizontal frictional surface, and
released. The coefficient of friction of the surface is μ = 0.15. How long does it
take before the cylinder starts to roll without slipping? What distance does the
cylinder travel between its release point and the point at which it commences to
roll without slipping?
Answer: Let v be the velocity of the cylinder’s centre of mass, ω the cylinder’s
angular velocity, f the frictional force exerted by the surface on the cylinder, M
the cylinder’s mass, and I the cylinder’s moment of inertia. The cylinder’s trans-
lational equation of motion is written
M ̇v = f.
Note that the friction force acts to accelerate the cylinder’s translational motion.
Likewise, the cylinder’s rotational equation of motion takes the form
I ω ̇ = −f b,