ch06 - Chapter 6 Kinematics of Rigid Bodies Undergoing...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Chapter 6 Kinematics of Rigid Bodies Undergoing Planar Motion 6.1 Relative Velocities on a Rigid Body 101 6.1.1 GOAL: Determine the angular velocity of the rollers supporting a bikes rear wheel. GIVEN: Size and configuration of the wheel and rollers. DRAW: FORMULATE EQUATIONS: We know from geometry that both rollers will have the same angular velocity and thus well concentrate on R 2 . We know that if the tire and roller roll without slip on each other that the velocity of the contact point is the same for each body. * v C = * v A + 1 * k * r C / A = 0 + 1 * b 3 (- r 1 * b 1 ) =- r 1 1 * b 2 * v C = * v B + 2 * b 3 * r C / B = 0 + 2 * b 3 ( r 2 * b 1 ) = r 2 2 * b 2 Equating these two velocity expressions for C gives us- r 1 1 = r 2 2 2 =- r 1 r 2 ! 1 The angular velocity of the rollers is therefore given by- (24 rad/s) r 1 r 2 * k 102 6.1.2 GOAL: Find || * v A || at t = 3 s. GIVEN: ( t ) and * r A / O . DRAW: FORMULATE EQUATIONS: * v B = * v A + * k * r A / O SOLVE: To solve the problem well need to derive an expression for . = (1- e at ) rad =- ae at rad We can now use this in our expression for velocity. * v A = r * e r + r * e =- are at rad Using our given data gives us * v A =- (- . 8 s- 1 )(1 m) e (- . 8 s- 1 )(3 . s ) rad = 7 . 26 10- 2 * k m/s || * v A || = 7 . 26 10- 2 m/s 103 6.1.3 GOAL: Find the rotational speed of the wheels in a microwave oven turntable. GIVEN: Dimensions and orientations of wheels and support plate. DRAW: FORMULATE EQUATIONS: Well use the formula for speed on a rotating body: * v B = * v A + * * r B / A ASSUME: At the point of contact between the wheels and the support plate we have equal velocities, a consequence of the no-slip condition. SOLVE: First well determine the angular speed of the support plate from knowing its period of rotation: P = 2 10 s = 5 rad/s Now well equate the velocity of the contact point C as found from the center of the supporting wheel ( A ) and from the center of the support plate ( O ). * v C = * v C * v A + W * (0 . 5 cm) * k = * v O + P * k (12 cm) * (0 . 5 cm) W * =- (12 cm) P * W =- 24 P W =- 24 P =- 24 5 rad/s 104 6.1.4 GOAL: Determine the velocity of a linear rack thats connected by two gears to another rack. GIVEN: Size and configuration of the two meshing gears and racks. DRAW: FORMULATE EQUATIONS: We know that where the gear teeth mesh they move at the same velocity. C 1 , C 2 and C 2 are our three points of contact and were given that * v C 1 = v A * * v C 1 = * v O 1 + 1 * k * r C 1 /O 1 = 0 + 1 * k (- r 1 * ) =- r 1 1 * Equating these two velocity expressions for C 1 gives us v A =- r 1 1 1 =- v A r 1 Next look at the point C 2 : * v C 2 = * v O 1 + 1 * k * r C 2 /O 1 = 0 +- v A r 1 !...
View Full Document

Page1 / 152

ch06 - Chapter 6 Kinematics of Rigid Bodies Undergoing...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online