DYNAMICS OF RIGID BODIES
TYPES OF MOTION
1. Translational motion – is the motion by which a
body shifts from one point in space to another
a. Rectilinear motion – motion of a particle along
a straight line
b. Curvilinear motion – motion occurs when a
particle travels along a curved path
2. Rotational motion – is the motion by which a body
moves in circles a
3. Periodic Motion - is the motion by which a body
vibrates or oscillates back and forth, over the same
path.
ROTATIONAL MOTION
ROTATIONAL MOTION
Angular Velocity,w – defined as the rate of change of
angular position
Angular acceleration,a – defined as the rate of change of
angular velocity
2
∆𝜃 𝐴 = 𝜋𝑟 ∆𝜔
𝜔= 𝛼=
∆𝑡 ∆𝑡
LINEAR TO ROTATIONAL
𝑉 = 𝑟𝜔 𝑎𝑡 = 𝑟𝛼 𝑎𝑛 = 𝜔2 𝑟
Uniformly Accelerated Motion Constant Angular Acceleration
𝑎𝑡 2 𝛼𝑡 2
𝑠 = 𝑣𝑜 𝑡 + 𝜃 = 𝜔𝑜 𝑡 +
2 2
𝑣𝑓 2 = 𝑣𝑜 2 + 2𝑎𝑠 𝜔𝑓 2 = 𝜔𝑜 2 + 2𝛼𝜃
𝑣𝑓 = 𝑣𝑜 + 𝑎𝑡 𝜔𝑓 = 𝜔𝑜 + 𝛼𝑡
𝐴 = 𝜋𝑟 2
Period T – defined as the time required for one complete
revolution 2𝜋
𝑇=
𝜔
Frequency, f – defined as the number of complete revolution
per second
1 𝜔
𝑓= =
𝑇 2𝜋
Problem 1
The car A has a forward speed of 18kph and is
accelerating at 3m/s2. The angular rate 𝜔 =3 rev/min of
the Ferris wheel is constant. Determine the:
A. velocity of the car relative to the observer B, who
rides in a non-rotating chair of the Ferris wheel.
B. acceleration of the car relative to the observer B,
who rides in a non-rotating chair of the Ferris wheel.
Problem 1
The car A has a forward speed of 18kph and is accelerating at 3m/s. The angular rate 𝜔 =3
rev/min of the Ferris wheel is constant. Determine the:
a. velocity of the car relative to the observer B, who rides in a non rotating chair of the
Ferris wheel.
b. acceleration of the car relative to the observer B, who rides in a non rotating chair of the
Ferris wheel.
Problem 2
The angle between the 2-m bar and the x-axis varies
according to the equation θ = 0.3t3 - 1.6t + 3 where θ is in
radians and t is in seconds. When t = 2 seconds, assume
the rotates from its end.
A. Determine the tangential acceleration at the end of
the bar
B. Determine the centripetal acceleration at the end of
the bar
C. Determine the total acceleration at the end of the
bar.
Problem 3
A bicycle slows down uniformly from vo = 8.4 m/s to
rest over a distance of 115 m. Each wheel and tire have
an overall diameter of 68 cm. Determine
A. The angular velocity of the wheels at the initial
instant.
B. The total number of revolutions each wheel rotates
before coming to rest.
C. The angular acceleration of the wheel.
D. The time it took the bicycle to come to a stop.
Problem 3
A bicycle slows down uniformly from vo = 8.4 m/s to rest over a distance of 115 m.
Each wheel and tire have an overall diameter of 68 cm. Determine
A. The angular velocity of the wheels at the initial instant.
B. The total number of revolutions each wheel rotates before coming to rest.
C. The angular acceleration of the wheel.
D. The time it took the bicycle to come to a stop.
Problem 4
At t = 0, a grinding wheel has an angular velocity of 24 rad/s. It
has a constant angular acceleration of 30 rad/s2 until a circuit
breaker trips at t = 2 seconds. From then on, it turns through 432
rad as it coasts to a stop at constant angular acceleration.
A. Through what total angle did the wheel turn between t = 0 and
the time it stopped?
B. What was its acceleration as it slowed down?
C. At what time did it stop?
