Question

A grindstone of mass M = 30 kg and radius 0.5 m has a constant
acceleration, ", of 3.0 rad/s2. After 2 seconds....

A. Find the angular displacement
B. Find the angular speed, T, after two seconds.
C. Find the distance traveled in meters of a point on the rim of the
grindstone after two seconds.
D. Find the linear (or tangential) speed, v, of a point on the rim after
two seconds.
E. Find the tangential acceleration of a point on the rim after two
seconds.
F. Find the centripetal acceleration of a point on the rim after two
seconds.
G. If the grindstone is considered a solid disc with a Moment of Inertia,
I, is given by the formula MR2/2, find the torque that is necessary for it to
have the give angular acceleration.

please i need the work with answers

Answer 1

Answer 2

a. theta=0.5*alpha*t²

theta=0.5*3*4 = 6 rad

b. w=alpha*t

w=3*2 = 6 rad/sec

c. l=r*theta = 0.5*6 = 3m

d. v=rw

v=0.5*6 = 3 m/s

e. a=r*alpha = 0.5*3 =1.5 m/s^2

f. a=v²/r = 9/0.5 = 18 m/s²

g. torque=I*alpha

torque = (30*0.5*0.5/2)*3 = 11.25 Nm

Answer 3