Rigid Bodies

Rotation

Gears

What motion is this?

100

A car turning a corner

Translation (Curvilinear)

200

A disk is rotating at 𝟒𝒓𝒂𝒅/𝒔 . If it is subjected to constant angular acceleration of 2 𝑟𝑎𝑑/𝑠 2 determine the acceleration at B.

∝ = (-4i+32j) ft/s^s

200

When the gear rotates 20 revolutions, it achieves an angular velocity of w = 30 rad/s, starting from rest. Determine its constant angular acceleration and the time required.

angular acceleration = 3.58 rad/s²

t = 8.38 s

200

A basketball being shot

Translation (Curvilinear)

300

The fan blades suddenly experience an angular acceleration of 2 rad/𝑠 2 . If the blades are rotating with an initial angular velocity of 4𝑟𝑎𝑑/𝑠, determine the speed of point P when the blades have turned 2 revolutions.

14.2 ft/s

300

A motor gives gear A an angular acceleration of ∝_A = (4t³) rad/s², where t is in seconds. If this gear is initially turning at (ω_A)₀ = 20 rad/s, determine the angular velocity of gear B when t = 2s.

w_B(2) = 12 rad/s

300

Tire rolling across the floor

General Plane Motion

400

a_T= 3.5 j

400

A motor gives gear A an angular acceleration of ∝_A = (2t³) rad/s², where t is in seconds. If this gear is initially turning at ω_A = 15 rad/s, determine the angular velocity of gear B when t = 3s.

ω_A = 31.7 rad/s

400

A tire stuck in the mud

Rotational

500

a_N= -115.95 i

500

For a short period of time, the motor turns gear A with a constant angular acceleration of ∝A = 4.5 rad/s2, starting from rest. Determine the velocity of the cylinder and the distance it travels in 3 seconds. The cord is wrapped around pulley D which is rigidly attached to gear B.

V_C = 0.5625 m/s

S_C= 844 mm